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NCERT Class 12 Physics Chapter 7 Notes Alternating Current - Download PDF

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NCERT Class 12 Physics Chapter 7 Notes Alternating Current - Download PDF

Edited By Vishal kumar | Updated on Feb 02, 2024 05:13 PM IST

In Class 12 Physics, Chapter 7 on alternating current is essential not only for school exams, but also for engineering and medical entrance exams. These class 12 physics chapter 7 notes cover important topics such as power in an AC circuit and transformer principles, which are required for exams such as JEE Main and NEET. Aside from exams, understanding concepts such as Capacitor Applied to AC Voltage and LCR Circuit Applied to AC Voltage is essential for practical applications in medical instrumentation and electrical engineering.

These Alternating Current class 12 notes, available online through platforms such as Careers360, provide students with a thorough understanding of alternating current, bridging theoretical knowledge with real-world application. By mastering these topics, students not only prepare for academic success but also gain the skills required to succeed in engineering and medicine. So, these cbse class 12 physics ch 7 notes serve as indispensable tools for aspiring professionals, guiding them toward achievement in both exams and future careers.

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NCERT Class 12 Physics Chapter 7 Notes

Alternating Voltage:-

The voltage whose magnitude and direction changes with time and attains the same magnitude and direction after a definite time interval is called an ‘ alternating voltage’. Taking the expression for the induced emf e=e0sinωt, the alternating voltage can be expressed as

{"backgroundColor":"#ffffff","type":"$$","backgroundColorModified":false,"aid":null,"id":"2","code":"$$V\\,=\\,V_{0}\\sin \\omega t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,.......\\left(i\\right)$$","font":{"size":11,"color":"#000000","family":"Arial"},"ts":1636192242590,"cs":"mERDzGMk27Obe8cRFfkJAA==","size":{"width":226,"height":16}}

Where V₀ is the maximum (or peak) value of voltage.

Alternating Current:-

Due to this alternating voltage, the current that flows through the circuit also changes continuously between zero and maximum value and flows in one direction in the first half rotation and in the opposite direction in the next half rotation. This type of current is called an ‘ alternating current’. The alternating current may be expressed as

{"id":"3","backgroundColor":"#ffffff","backgroundColorModified":false,"code":"$$i\\,=\\,i_{0}\\sin \\omega t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,......\\left(ii\\right)$$","aid":null,"font":{"size":11,"color":"#000000","family":"Arial"},"type":"$$","ts":1636192221756,"cs":"bZFJ0y+7xxnI6sr96OCMzQ==","size":{"width":193,"height":16}}

Where i₀ is the maximum (or peak) value of current.

We get a sine curve (as shown in fig) when we plot the graph between the alternating voltage V or alternating current i and time t.1644568259228

Some Important Terms Regarding The Alternating Current

  • Maximum value or Peak value:- In a magnetic field a coil is rotating which produces the alternating voltage or current is maximum at two positions of the coil. This maximum value of alternating current or alternating voltage is known as the peak value of voltage or current. As shown in the above fig. It is represented by V₀ or i₀ respectively.

  • Periodic Time:- The time taken by the alternating current to complete one cycle is called the periodic time of the current. If in Eqn (i) or (ii), t is increased by 2?/?. The value of V or i remains unchanged. The periodic time of alternating current is

{"aid":null,"font":{"family":"Arial","size":11,"color":"#000000"},"backgroundColor":"#ffffff","code":"$$T\\,=\\,\\frac{2\\pi}{\\omega}$$","id":"4","backgroundColorModified":false,"type":"$$","ts":1636192572589,"cs":"NoU8A8FOLZl+RS8Y61E+NA==","size":{"width":64,"height":34}}

  • Frequency:- The number of cycles completed by an alternating current in one second is called the frequency of the current. It is equal to the number of rotations completed by the coil in one second. If the periodic time of the alternating current be T, then its frequency is

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{"backgroundColorModified":false,"backgroundColor":"#ffffff","id":"5","code":"\\begin{align*}\n{f\\,}&={\\,\\frac{1}{T}}\\\\\n{}&\\relempty{\\therefore f\\,=\\,\\frac{\\omega}{2\\pi}\\,}\\\\\n{\\,}&\\relempty{}\t\n\\end{align*}","font":{"color":"#000000","size":11,"family":"Arial"},"aid":null,"type":"align*","ts":1636193132248,"cs":"VJ52QohQE4XCTCLmvrm7IQ==","size":{"width":112,"height":70}}

Mean Value of An Alternating Current

An alternating current flows during a one-half cycle in one direction and during the other half-cycle in the opposite direction. So, the mean (or average) value of alternating current is zero for one complete cycle.

The mean value of alternating current over a half cycle is a finite quantity and quantity which is defined as the mean value of alternating. It is given by

{"backgroundColor":"#ffffff","code":"\\begin{lalign*}\n&{\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,i_{m\\,}=\\,\\frac{2}{\\pi}i_{0}\\,=\\,0.637i_{0}}\\\\\n&{\\,\\,\\,\\,\\,}\t\n\\end{lalign*}","backgroundColorModified":false,"type":"lalign*","font":{"family":"Arial","color":"#000000","size":11},"id":"8","aid":null,"ts":1636202416842,"cs":"2FjMG20GMGW8l3cz+WYvtQ==","size":{"width":154,"height":34}}



Thus, the mean value of a.c. for a half-cycle(t = 0 to = T/2) is 0.637 times, or 63.7% of the peak value.

similarly, the mean value of ac for the other half-cycle will be (t = T/2 to T) will be -2i0/Π=-0.637i0. It is zero for the full cycle.

Root mean square value of alternating current: The root-mean-square value of an alternating current is defined as the square root of the average of i² during a complete cycle, where i is the instantaneous value of the alternating current.

The root mean square you are the alternating current is given by

{"code":"$$i_{rms\\,}=\\,{\\sqrt[]{\\bar{i^{2}}}}\\,=\\,\\frac{i_{0}}{{\\sqrt[]{2}}\\,}=\\,0.707i_{0}$$","font":{"color":"#000000","size":11,"family":"Arial"},"backgroundColorModified":false,"id":"12","type":"$$","aid":null,"backgroundColor":"#ffffff","ts":1636197061833,"cs":"ShMjtC3YwHPfubBrccYMag==","size":{"width":225,"height":42}}

Thus, the root means the square value of an alternating current is 0.707 times and 70.7% of the peak value.

Similarly, the root mean square value of an alternating voltage represented by V = V₀ sin?t is given by

{"aid":null,"type":"$$","backgroundColor":"#ffffff","id":"13","font":{"family":"Arial","size":11,"color":"#000000"},"code":"$$V_{rms}\\,=\\,\\frac{V_{0}}{{\\sqrt[]{2}}}\\,=\\,0.707V_{0}$$","backgroundColorModified":false,"ts":1636197419352,"cs":"3Uq+gPkDxn3w9OqstOkYWQ==","size":{"width":174,"height":40}}

The phase difference between voltage and current i in an alternating current circuit

In some circuits, the current reaches its maximum value before the voltage becomes maximum. Then it is said the current is leading the voltage in phase. In some other circuits, the current reaches its maximum value after the voltage has become maximum. In such cases, the current is said to be lagging behind the voltage in phase.

If the alternating current circuit the voltage and the currents are in the same phase is that when the voltage is maximum the current is also maximum and when the voltage is zero the current is also zero then the alternating voltage and the alternating current are represented by the following equations

{"backgroundColor":"#ffffff","backgroundColorModified":null,"id":"14","code":"$V\\,=\\,V_{0}\\sin \\omega t$","aid":null,"font":{"color":"#000000","family":"Arial","size":11},"type":"$","ts":1636198510434,"cs":"keQX3z6NXLyQV5rpFwerSQ==","size":{"width":100,"height":13}}

{"backgroundColor":"#ffffff","backgroundColorModified":false,"aid":null,"id":"15","type":"$$","code":"$$i\\,=\\,i_{0}\\sin \\omega t$$","font":{"family":"Arial","size":11,"color":"#000000"},"ts":1636198539840,"cs":"l/EqJru5W07NNKDPnx5/yA==","size":{"width":89,"height":13}}

If in an alternating current circuit the current leads the voltage V by a phase difference ϕ then the expression for the voltage and the current will be written as follows

{"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","font":{"family":"Arial","color":"#000000","size":11},"id":"16-0","aid":null,"code":"$$V\\,=\\,V_{0}\\sin \\omega t$$","ts":1636198687131,"cs":"SNG+qRVu0RiKeLB7jsl/UQ==","size":{"width":100,"height":13}}

{"code":"$$i\\,=\\,i_{0}\\sin\\left(\\omega t\\,+\\,\\phi\\right)$$","id":"17-0","aid":null,"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","font":{"size":11,"family":"Arial","color":"#000000"},"ts":1636198760616,"cs":"S9vhwk5CgzNBFGRxVPBOLw==","size":{"width":138,"height":16}}

The graphical representation is shown in fig 2.

1644568261000

If in a circuit the alternating current i lags behind the alternating voltage by a phase difference ϕ. Then,

{"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","font":{"family":"Arial","color":"#000000","size":11},"id":"16-1","aid":null,"code":"$$V\\,=\\,V_{0}\\sin \\omega t$$","ts":1636198687131,"cs":"zBvypbF5Dx33bkkjBCzZOw==","size":{"width":100,"height":13}}

{"aid":null,"font":{"size":11,"color":"#000000","family":"Arial"},"backgroundColor":"#ffffff","code":"$$i\\,=\\,i_{0}\\sin\\left(\\omega t\\,-\\,\\phi\\right)$$","backgroundColorModified":false,"id":"17","type":"$$","ts":1636198997352,"cs":"fl9KYyMSf28GQCojQiZpWw==","size":{"width":138,"height":16}}

This graphical representation is shown in fig 3.

1644568258856

Phasors and Phasor diagrams:- The (rotating) vectors representing current and voltage are called phasors.

Phasor diagrams show alternating current and alternating voltage with their phase angles as rotating vectors (phasors).

Different Types of A.C. Circuits

i. A circuit containing resistance only: let an alternating voltage V is given by

{"aid":null,"backgroundColorModified":false,"id":"16-2","type":"$$","font":{"family":"Arial","color":"#000000","size":11},"backgroundColor":"#ffffff","code":"$$V\\,=\\,V_{0}\\sin \\omega t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,.....\\left(i\\right)$$","ts":1636200246425,"cs":"SZaCkD4SSctpzo0VDXmAMw==","size":{"width":194,"height":16}}

And the peak value of the current in the circuit

1644569217491

{"backgroundColorModified":false,"id":"19","aid":null,"type":"$$","code":"$$\\therefore i\\,=\\,i_{0}\\sin \\omega t\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,......\\left(ii\\right)$$","font":{"size":11,"family":"Arial","color":"#000000"},"backgroundColor":"#ffffff","ts":1636200298232,"cs":"wvI0vB6o8Zgxmx+UPl21Cw==","size":{"width":228,"height":16}}

A comparison of equation (ii) with equation (i) shows that in a pure resistor the current I is always in phase with the applied voltage V . Figure (a) shows the phase relationship graphically and fig (b) is the phasor diagram for alternating voltage and current.

A comparison of equation (ii) with equation (i) shows that in a pure resistor the current I is always in phase with the applied voltage V . Figure (a) shows the phase relationship graphically and fig (b) is the phasor diagram for alternating voltage and current.

1644569250021

ii. A circuit containing inductance only: Let an alternating voltage is given by

{"backgroundColor":"#ffffff","backgroundColorModified":null,"id":"14","code":"$V\\,=\\,V_{0}\\sin \\omega t$","aid":null,"font":{"color":"#000000","family":"Arial","size":11},"type":"$","ts":1636198510434,"cs":"keQX3z6NXLyQV5rpFwerSQ==","size":{"width":100,"height":13}}

1644569356561

The maximum current in the circuit,

{"type":"lalign*","id":"24","backgroundColor":"#ffffff","font":{"color":"#000000","size":11,"family":"Arial"},"code":"\\begin{lalign*}\n&{i\\,=\\,\\frac{V_{0}}{\\omega L}\\sin\\left(\\omega t-\\,\\frac{\\pi}{2}\\right)}\t\n\\end{lalign*}","aid":null,"backgroundColorModified":false,"ts":1636203093154,"cs":"20YgYLX0T+wV/UJW8878aw==","size":{"width":164,"height":34}}


Where i₀ = ( V₀/⍵L) is the peak value of current. Comparison of this equation with the voltage equation shows that in a pure inductor the current lags behind the voltage by a phase angle of ?/2. This means that when voltage is maximum the current is zero and vice versa. Fig 5 (a) shows this phase relationship graphically and figure 5 (b) shows the phasor diagram AC circuit containing inductance only.

1644569283501

Inductive Reactance:- By applying Ohm’s law in the eqn of the peak value of the current in the coil i0=V0/?L we find that ?L has thedimension of resistance which is known as ‘ reactance of the coil’ or inductive reactance. It is denoted by XL.


1644569284246

{"font":{"family":"Arial","size":11,"color":"#000000"},"backgroundColorModified":false,"backgroundColor":"#ffffff","type":"$$","code":"$$X_{L}\\,=\\,\\omega L\\,=\\,2\\pi fL$$","id":"27","aid":null,"ts":1636206963060,"cs":"SbBpKW6Tx0jTbbu/r4OSCQ==","size":{"width":140,"height":14}}

Where f is the frequency of the alternating current. Thus, the inductive reactance increase with the increasing frequency of the current

When L is in henry and f is in hertz and XL is in ohm.

iii. Circuit containing Capacitance only:- The alternating Voltage is given by

{"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","font":{"family":"Arial","color":"#000000","size":11},"id":"16-0","aid":null,"code":"$$V\\,=\\,V_{0}\\sin \\omega t$$","ts":1636198687131,"cs":"SNG+qRVu0RiKeLB7jsl/UQ==","size":{"width":100,"height":13}}1644569480246







The maximum current in the circuit

{"id":"29","aid":null,"backgroundColor":"#ffffff","type":"$$","code":"$$i\\,=\\,i_{0}\\left(\\omega t\\,+\\frac{\\pi}{2}\\right)$$","font":{"color":"#000000","size":11,"family":"Arial"},"backgroundColorModified":false,"ts":1636208257558,"cs":"RkoU6vf1+wgZXaxIZ6BcMw==","size":{"width":121,"height":30}}



Where I0=V0/(1/?C) is the peak value of the current.

Comparing this equation with the voltage equation shows that in a perfect capacitor, the current leads by the voltage by a phase angle of ?/2 or we can say that the voltage lags behind the current by a phase angle of ?/2. This means that when the voltage is zero, the current is maximum and vice versa. Fig 6(a) shows the phase relationship graphically and fig6(b) is the phasor diagram of a.c. a circuit containing C only.

1644569480990


Capacitive Reactance:- On applying Ohm’s law in the eqn of the peak value of the current in the coil I0=V0/(1/?C) we find that 1/?C has the dimension of resistance which is known as reactance of the capacitor or capacitive reactance. It is denoted by XC

{"id":"31","code":"$$X_{C}\\,=\\,\\frac{1}{\\omega C}\\,=\\,\\frac{1}{2\\pi fC}$$","aid":null,"font":{"size":11,"color":"#000000","family":"Arial"},"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","ts":1636208961734,"cs":"eFDWgLCviBLIFkYsXmlsPw==","size":{"width":158,"height":37}}1644569658772

Where f is the frequency of the alternating current. Thus, the capacitive reactance decrease with increasing frequency of the current. The graph between XC and f is a rectangular hyperbola.

When C is in farad and f is in hertz then XC=1/2?fC is in ohm


iv. Circuit containing Inductance and Resistance in series(L-R series circuit). Let an alternating voltage V=V0sin?t be applied to a circuit containing an inductance L and a non-inductive resistance R are in series as shown in fig. The same current will flow both in L and R.

Let i the current in the circuit at any instant and VL and VR. The potential difference across L and R respectively at that instant. Then16445699058341644569905355

{"backgroundColor":"#ffffff","type":"$$","font":{"family":"Arial","color":"#000000","size":11},"id":"35","backgroundColorModified":false,"code":"$$V_{L\\,}\\,=\\,iX_{L}$$","aid":null,"ts":1636209962853,"cs":"ZvrKROY0pk3aEcCC+lVY9w==","size":{"width":77,"height":13}}

{"type":"$$","id":"36","backgroundColorModified":false,"backgroundColor":"#ffffff","aid":null,"font":{"family":"Arial","color":"#000000","size":11},"code":"$$V_{R}\\,=iR$$","ts":1636209986530,"cs":"/tKhI3t7Tjtsg8lWm/tYtA==","size":{"width":64,"height":13}}

Where XL is the inductive reactance now VR is in phase with the current i, while VLleads i by 90° Thus, VR and VL

are mutually at right angles.

The phasor diagram is drawn in the figure. In this diagram, the vector represents VR while OB represents VL. The vector OD represents the resultant of VR and VL which is applied voltage V.

{"backgroundColor":"#ffffff","backgroundColorModified":false,"code":"\\begin{lalign*}\n&{V^{2\\,}\\,=\\,V_{R}^{2}\\,+\\,V_{L}^{2}}\\\\\n&{V^{2\\,}=\\,i^{2}\\left(R^{2}\\,+\\,X_{L}^{2}\\right)}\\\\\n&{i\\,=\\frac{V}{{\\sqrt[]{R^{2\\,}+\\,X_{L}^{2}}}}}\t\n\\end{lalign*}","font":{"size":11,"family":"Arial","color":"#000000"},"type":"lalign*","aid":null,"id":"42-0","ts":1636210622531,"cs":"NHPzyUaYefPMRyLTYfok4A==","size":{"width":144,"height":105}}

According to Ohm's law, a circuit's effective resistance is

{"code":"$${\\sqrt[]{\\left(R^{2}+X_{L}^{2}\\right)}}$$","backgroundColor":"#ffffff","font":{"size":11,"family":"Arial","color":"#000000"},"aid":null,"backgroundColorModified":false,"id":"43-0-0","type":"$$","ts":1636210747538,"cs":"Ueny3/XX2fQyvGjSzYbJQw==","size":{"width":96,"height":30}}. We can decode it as Z, which is the impedance of the circuit. Hence, we have L - R circuit.

{"backgroundColor":"#ffffff","aid":null,"id":"43-1-0-0","code":"$$Z\\,=\\,{\\sqrt[]{\\left(R^{2}+X_{L}^{2}\\right)}}$$","type":"$$","backgroundColorModified":false,"font":{"color":"#000000","family":"Arial","size":11},"ts":1636210924472,"cs":"+bUMkdawexrw6hLjEs3fYA==","size":{"width":137,"height":30}}


But {"font":{"family":"Arial","color":"#000000","size":11},"type":"$$","backgroundColor":"#ffffff","backgroundColorModified":false,"id":"44-0","code":"$$X_{L\\,}\\,=\\,\\omega L$$","aid":null,"ts":1636210967843,"cs":"dLewGTO1BjSI1pH4OEUazw==","size":{"width":76,"height":13}}

{"id":"43-1-1-0","type":"$$","backgroundColorModified":false,"font":{"color":"#000000","size":11,"family":"Arial"},"code":"$$\\therefore Z\\,=\\,{\\sqrt[]{\\left(R^{2}+\\left(\\omega L\\right)_{}^{2}\\right)}}$$","backgroundColor":"#ffffff","aid":null,"ts":1636211052460,"cs":"izrtNSX2ZWJ+XUx4eXEwbA==","size":{"width":178,"height":40}}

The quantity Z is measured in ohm is called impedance because it impedes the flow of alternating current in the circuit.

The reciprocal of the impedance is called the admittance of the AC circuit. It is measured in mho or ohm-¹ (Ω-¹) or siemens (S).

The phasor diagram shows in L - R circuit the applied voltage V leads the current i (or the current i, lags behind the voltage V) by a phase angle ϕ given by

{"font":{"family":"Arial","color":"#000000","size":11},"backgroundColor":"#ffffff","type":"lalign*","backgroundColorModified":false,"aid":null,"code":"\\begin{lalign*}\n&{\\tan \\phi=\\,\\frac{V_{L}}{V_{R}}\\,=\\,\\frac{iX_{L}}{iR}\\,=\\frac{X_{L}}{R}\\,}\\\\\n&{\\tan \\phi=\\,\\frac{\\omega L}{R}}\t\n\\end{lalign*}","id":"45","ts":1636211553217,"cs":"+6RLZSavVu7akj2GNoeTlw==","size":{"width":210,"height":77}}

It is clear from the situation that if L = 0, then ϕ = 0( the voltage and the current will be in the same phase): If R = 0 then ϕ = 90° (the voltage will lead the current by 90° ).

v. A circuit containing capacitance and resistance in series:- in this case, the instantaneous potential difference across C and R are given by VC=iXC and VR=iR where XC is the capacitive reactance and i is the instantaneous current.

16445699008771644569901714

Now, VR is in the phase with i while VC lags behind i by 90°. The phasor diagram is drawn in the figure in which the vector OA represent VR and the vector OB represents VC the vector OD represents the resultant of VR and VCwhich is applied voltage V. Thus,


{"aid":null,"backgroundColor":"#ffffff","code":"\\begin{lalign*}\n&{V^{2\\,}\\,=\\,V_{R}^{2}\\,+\\,V_{C}^{2}}\\\\\n&{V^{2\\,}=\\,i^{2}\\left(R^{2}\\,+\\,X_{C}^{2}\\right)}\\\\\n&{i\\,=\\frac{V}{{\\sqrt[]{R^{2\\,}+\\,X_{C}^{2}}}}}\t\n\\end{lalign*}","type":"lalign*","backgroundColorModified":false,"font":{"family":"Arial","size":11,"color":"#000000"},"id":"42-1","ts":1636212383205,"cs":"oJi96vC/Mt4rGBVHBFQKPw==","size":{"width":145,"height":105}}

Applying Ohm's law we see that

{"type":"$$","backgroundColorModified":false,"id":"43-0","code":"$${\\sqrt[]{\\left(R^{2}+X_{C}^{2}\\right)}}$$","font":{"family":"Arial","color":"#000000","size":11},"aid":null,"backgroundColor":"#ffffff","ts":1636212420048,"cs":"wFrlzjajwf8vRlUSx1rLmg==","size":{"width":96,"height":30}}

is the effective resistance of the circuit. It is called the impedance of the circuit and is represented by Z. Thus, in C - R circuit we have

{"backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","font":{"size":11,"family":"Arial","color":"#000000"},"code":"$$Z\\,=\\,{\\sqrt[]{\\left(R^{2}+X_{C}^{2}\\right)}}$$","id":"43-1-0","aid":null,"ts":1636212444187,"cs":"WsWGWQss+hEBjxeOIaMwuA==","size":{"width":137,"height":30}}

But

{"type":"$$","backgroundColor":"#ffffff","font":{"size":11,"color":"#000000","family":"Arial"},"code":"$$X_{L\\,}\\,=\\,1/\\omega C$$","aid":null,"backgroundColorModified":false,"id":"44-1","ts":1636212463316,"cs":"cjysR4ub6eD2kvBeTH5bSg==","size":{"width":94,"height":16}}

{"aid":null,"backgroundColor":"#ffffff","code":"$$\\therefore Z\\,=\\,{\\sqrt[]{\\left(R^{2}+\\left(1/\\omega C\\right)_{}^{2}\\right)}}$$","font":{"family":"Arial","size":11,"color":"#000000"},"backgroundColorModified":false,"id":"43-1-1-1","type":"$$","ts":1636212482108,"cs":"VCb4jFgQRBGo89IdcxOoyQ==","size":{"width":196,"height":40}}

The phasor diagram shows that in C R circuit the applied voltage V lacks behind the current i ( or the current i leads the voltage V) by a phase angle ϕ, given by

{"code":"\\begin{lalign*}\n&{\\tan \\phi=\\,\\frac{V_{C}}{V_{R}}\\,=\\,\\frac{X_{C}}{R}}\\\\\n&{\\tan \\phi=\\,\\frac{1/\\omega C}{R}}\t\n\\end{lalign*}","aid":null,"id":"53","backgroundColorModified":false,"type":"lalign*","font":{"color":"#000000","size":11,"family":"Arial"},"backgroundColor":"#ffffff","ts":1636212708841,"cs":"K2BIFsp/YIkw7bNPeWmSSw==","size":{"width":149,"height":80}}

vi. A circuit containing capacitance and Inductance (L-C Circuit):- In this case, the potential difference across L will lead the current i in the face by 90° while the potential difference {"font":{"family":"Arial","color":"#000000","size":11},"aid":null,"code":"$$V_{c}$$","id":"50","type":"$$","backgroundColor":"#ffffff","backgroundColorModified":false,"ts":1636212233329,"cs":"94Cccy6tv2pcRaX6au01qQ==","size":{"width":13,"height":13}} across C will lag behind the current i in phase by 90° the phasor diagram is drawn in the figure.

16445703471521644570346681


It meets the phase difference between VL and VC is shown 180 ° i.e, they are opposite in phase to each other. Hence the resultant potential difference and LC circuit is

{"type":"$$","aid":null,"backgroundColorModified":null,"backgroundColor":"#ffffff","id":"54","font":{"family":"Arial","color":"#000000","size":11},"code":"$$V\\,=\\,V_{L\\,}\\approx V_{C}$$","ts":1636269087465,"cs":"a9x6P8h80zSzUylAxGdgag==","size":{"width":104,"height":13}}

and the impedance of the circuit is

{"id":"55","font":{"size":11,"color":"#000000","family":"Arial"},"aid":null,"code":"$$Z\\,=\\,X_{L}\\,\\approxat{}\\,X_{C}$$","backgroundColor":"#ffffff","type":"$$","backgroundColorModified":false,"ts":1636269214453,"cs":"k8nNfcV11xOT14lGzBe5aw==","size":{"width":114,"height":13}}

if XL=XC then the impedance Z = 0 in this situation the amplitude of the current in the circuit would be infinite. It is the condition of electrical resonance. Thus, in the condition electrical resonance

{"code":"\\begin{lalign*}\n&{X_{L\\,}=\\,X_{C}}\\\\\n&{\\omega L\\,=\\,\\frac{1}{\\omega C}}\\\\\n&{2\\pi fL\\,=\\,\\frac{1}{2\\pi fC}}\\\\\n&{f^{2}\\,=\\,\\frac{1}{4\\pi^{2}LC}}\\\\\n&{f\\,=\\,\\frac{1}{2\\pi}{\\sqrt[]{\\frac{1}{LC}}}}\t\n\\end{lalign*}","type":"lalign*","id":"57","backgroundColorModified":false,"font":{"size":11,"family":"Arial","color":"#000000"},"aid":null,"backgroundColor":"#ffffff","ts":1636269565035,"cs":"l7bqftPvK2KvEjnsSjUqdQ==","size":{"width":113,"height":188}}

This is called a resonant frequency of the circuit.

vii. A circuit containing inductance capacitance and resistance in a series (LCR series circuit):- Let an alternating voltage V=V0sinωt be applied to a circuit containing an inductance L, a capacitance C, and resistance R all joined in series. As shown in fig. The same current i will flow in all three and the vector sum of the potential difference across them will be equal to the applied voltage.


1644570405906

Let i be the current in the circuit at any instant of time and VL, VC and VR are the potential difference across L, C and R respectively at that instant. Then

{"backgroundColorModified":false,"backgroundColor":"#ffffff","font":{"size":11,"color":"#000000","family":"Arial"},"type":"$$","code":"$$V_{L}\\,=\\,iX_{L}$$","id":"62","aid":null,"ts":1636270047589,"cs":"53bEtTL1jYcy9NCCKmntjA==","size":{"width":74,"height":13}}, {"backgroundColorModified":false,"aid":null,"type":"$$","id":"63","backgroundColor":"#ffffff","font":{"family":"Arial","size":11,"color":"#000000"},"code":"$$V_{C}\\,=\\,iX_{C}$$","ts":1636270085454,"cs":"ToGZ+1/nKuYkDbnuEWKq/w==","size":{"width":76,"height":13}} and {"backgroundColor":"#ffffff","backgroundColorModified":false,"aid":null,"id":"64","type":"$$","code":"$$V_{R}\\,=\\,iR$$","font":{"family":"Arial","color":"#000000","size":11},"ts":1636270105056,"cs":"TfyW0FuzJD0QzW4UbdRWCw==","size":{"width":66,"height":13}}


Now XL and XC are the inductive and capacitive reactance respectively.

Now VR is in phase with i but VL leads by 90°. The phasor diagram is drawn as a figure. In this diagram, the vector OA represents VR and the vector OB represents VL and the vector OC represents VC. VLand VC is opposite to each other. if VL>VC then their results will be VL-VCwhich is represented by OD. Finally, the vector OF represents the resultant of VR and VL-VC, ie., the resultant of all the three, which is applied voltage V. Thus

{"id":"78","backgroundColor":"#ffffff","backgroundColorModified":false,"type":"lalign*","aid":null,"font":{"family":"Arial","color":"#000000","size":11},"code":"\\begin{lalign*}\n&{V^{2}\\,=\\,V_{R}^{2}\\,+\\,\\left(V_{L}\\,-\\,V_{C}\\right)^{2}}\\\\\n&{V^{2}\\,=\\,i^{2}\\left(R^{2}\\,+\\,\\left(X_{L}\\,-\\,X_{C}\\right)\\right)}\\\\\n&{i\\,=\\,\\frac{V}{{\\sqrt[]{R^{2}\\,+\\,\\left(X_{L}\\,-\\,X_{C}\\right)^{2}}}}}\t\n\\end{lalign*}","ts":1636271300421,"cs":"w8sAR0W5j0vi5TI4jSutLw==","size":{"width":209,"height":106}}

Applying ohm's law we see that


{"code":"$${\\sqrt[]{R^{2}\\,+\\,\\left(X_{L}\\,-\\,X_{C}\\right)^{2}}}$$","backgroundColor":"#ffffff","id":"79","font":{"color":"#000000","family":"Arial","size":11},"aid":null,"type":"$$","backgroundColorModified":false,"ts":1636271335994,"cs":"OU2n56ARWSBoIVlCFbv31g==","size":{"width":156,"height":30}} is the effective resistance of the circuit and is called the impedance Z of the circuit. Thus, in the L-C-R circuit, we have

{"aid":null,"font":{"size":11,"family":"Arial","color":"#000000"},"id":"80","code":"$$Z\\,=\\,{\\sqrt[]{R^{2}\\,+\\,\\left(X_{L}\\,-\\,X_{C}\\right)^{2}}}$$","backgroundColorModified":false,"backgroundColor":"#ffffff","type":"$$","ts":1636271416373,"cs":"FawCDxnx/6acK8iFB6TGBA==","size":{"width":198,"height":30}}

{"aid":null,"backgroundColor":"#ffffff","font":{"family":"Arial","size":11,"color":"#000000"},"id":"81","type":"$$","backgroundColorModified":false,"code":"$$X_{L}\\,=\\,\\omega L$$","ts":1636271442399,"cs":"FkxAnPBKdKm/lWtgOVorXg==","size":{"width":72,"height":13}} and

{"font":{"size":11,"color":"#000000","family":"Arial"},"id":"82","type":"$$","code":"$$X_{C}\\,=\\,\\frac{1}{\\omega C}$$","backgroundColorModified":false,"aid":null,"backgroundColor":"#ffffff","ts":1636271468950,"cs":"gNyu6EsAk6rDf3oLfEDEBA==","size":{"width":81,"height":34}}

{"type":"$$","backgroundColorModified":false,"font":{"family":"Arial","color":"#000000","size":11},"id":"83-0","aid":null,"backgroundColor":"#ffffff","code":"$$\\therefore\\,\\,\\,\\,Z\\,=\\,{\\sqrt[]{R^{2}\\,+\\,\\left(\\omega L\\,-\\,\\frac{1}{\\omega C}\\right)^{2}}}$$","ts":1636271525771,"cs":"PrJPYBpU210+svL901UZxg==","size":{"width":244,"height":50}}


The phasor diagram (fig) shows that in the L-C-R circuit the applied voltage V leads the current i was a phase angle ϕ given by

{"id":"84","type":"lalign*","code":"\\begin{lalign*}\n&{\\tan \\phi=\\,\\frac{V_{L}-\\,V_{C}}{V_{R}}\\,=\\,\\frac{X_{L}\\,-\\,X_{C}}{R}}\\\\\n&{\\tan \\phi=\\,\\frac{\\omega L-\\,\\frac{1}{\\omega C}}{R}}\t\n\\end{lalign*}","aid":null,"backgroundColorModified":false,"backgroundColor":"#ffffff","font":{"family":"Arial","size":11,"color":"#000000"},"ts":1636271723254,"cs":"pvSRtES+Eoz1ckB0hqbFzA==","size":{"width":242,"height":84}}

The following three cases arise

When ωL>1/ωC then tanΦ is positive. In this case, the voltage V leads the current i.

When ωL<1/ωC then tanΦ negative. In this case, the voltage V lags behind the current i.

When ωL=1/ωC then tanΦ=0 in this case the voltage V and the current i are in the phase.

Again when ωL=1/ωC,

{"type":"$$","backgroundColor":"#ffffff","code":"$$\\therefore\\,\\,\\,\\,Z\\,=\\,{\\sqrt[]{R^{2}\\,+\\,\\left(\\omega L\\,-\\,\\frac{1}{\\omega C}\\right)^{2}}}\\,=\\,R$$","aid":null,"font":{"color":"#000000","family":"Arial","size":11},"id":"83-1","backgroundColorModified":false,"ts":1636272245968,"cs":"6INL0gPw3ZG5PtRG8IAAQw==","size":{"width":286,"height":50}}

Which is the minimum value Z can have. Thus, in case, impedance is minimum and hence the current is maximum. This is the case of electrical resonance. Hence, at resonance

{"aid":null,"type":"lalign*","backgroundColor":"#ffffff","id":"90","font":{"color":"#000000","size":11,"family":"Arial"},"backgroundColorModified":false,"code":"\\begin{lalign*}\n&{\\omega L\\,=\\,\\frac{1}{\\omega C}}\\\\\n&{\\omega\\,=\\,\\frac{1}{{\\sqrt[]{LC}}}}\t\n\\end{lalign*}","ts":1636272435318,"cs":"RlVJhDKtQHvjHs7+Ehss7w==","size":{"width":84,"height":80}}

But ω=2πf, where f is the frequency of the applied voltage. Therefore

{"backgroundColor":"#ffffff","code":"$$f\\,=\\,\\frac{1}{2\\pi{\\sqrt[]{LC}}}\\,=\\,f_{0}$$","backgroundColorModified":false,"aid":null,"type":"$$","font":{"family":"Arial","size":11,"color":"#000000"},"id":"92","ts":1636272541289,"cs":"snpXehPvWt2pOg1ns8ydnA==","size":{"width":144,"height":40}}

Where

{"id":"93","backgroundColor":"#ffffff","aid":null,"font":{"color":"#000000","size":11,"family":"Arial"},"type":"$$","backgroundColorModified":false,"code":"$$f_{0}\\,\\left(=\\frac{1}{2\\pi{\\sqrt[]{LC}}}\\right)$$","ts":1636272586780,"cs":"+hLCFRLhS4TWh/q2Ougc3w==","size":{"width":121,"height":41}}

is the natural frequency of the circuit when the resistance is zero.

The condition for resonance is the frequency of the applied voltage should be equal to the natural frequency of the circuit when the resistance of the circuit is zero.


1644570408696

Impedance triangle:- The impedance of an L-C-R a.c. the circuit is given by

{"aid":null,"font":{"size":11,"family":"Arial","color":"#000000"},"id":"80","code":"$$Z\\,=\\,{\\sqrt[]{R^{2}\\,+\\,\\left(X_{L}\\,-\\,X_{C}\\right)^{2}}}$$","backgroundColorModified":false,"backgroundColor":"#ffffff","type":"$$","ts":1636271416373,"cs":"FawCDxnx/6acK8iFB6TGBA==","size":{"width":198,"height":30}}

and the phase relationship is given by

{"backgroundColor":"#ffffff","id":"94","font":{"size":11,"family":"Arial","color":"#000000"},"backgroundColorModified":false,"aid":null,"code":"$$\\tan \\phi=\\,\\frac{X_{L}-X_{C}}{R}$$","type":"$$","ts":1636272789998,"cs":"udeMBFWIj8MkYbgIiW+5lg==","size":{"width":136,"height":34}}

this triangle is called the impedance triangle.

Power in A.C. Circuit:-

(i) Circuit containing pure resistance only:-

{"font":{"size":11,"color":"#000000","family":"Arial"},"id":"95-0","type":"$$","backgroundColor":"#ffffff","aid":null,"code":"$$\\bar{P}=\\,\\frac{1}{2}V_{0}i_{0}\\,=\\,\\frac{V_{0}}{{\\sqrt[]{2}}}\\,\\frac{i_{0}}{{\\sqrt[]{2}}}$$","backgroundColorModified":false,"ts":1636274873685,"cs":"7VHXU216F1fQNgYcEGiwSA==","size":{"width":176,"height":40}}


{"aid":null,"code":"$$\\bar{P}\\,=\\,V_{rms}\\,\\times\\,i_{rms}$$","type":"$$","id":"96","backgroundColorModified":false,"font":{"size":11,"family":"Arial","color":"#000000"},"backgroundColor":"#ffffff","ts":1636274938977,"cs":"VCEZ4Os8vZDZf3uhqKMQyQ==","size":{"width":128,"height":16}}

(ii) Circuit containing both inductance and resistance (L-R) circuit:-


{"code":"$$\\bar{P}=\\,\\frac{1}{2}V_{0}i_{0}\\,\\cos \\phi=\\,\\frac{V_{0}}{{\\sqrt[]{2}}}\\,\\frac{i_{0}}{{\\sqrt[]{2}}}\\,\\cos \\phi$$","font":{"family":"Arial","color":"#000000","size":11},"type":"$$","backgroundColor":"#ffffff","id":"95-1","backgroundColorModified":false,"aid":null,"ts":1636275237023,"cs":"q+WVvpplh5bXpsoUZGjAVA==","size":{"width":257,"height":40}}


{"aid":null,"id":"97","code":"$$\\bar{P}\\,=\\,V_{rms}\\times i_{rms}\\times\\,\\cos \\phi$$","backgroundColorModified":false,"font":{"size":11,"family":"Arial","color":"#000000"},"type":"$$","backgroundColor":"#ffffff","ts":1636275314288,"cs":"HjCJZtss6L5+xKaCOK23kQ==","size":{"width":185,"height":16}}


cosΦ is known as the power factor of the circuit. Its value depends on the nature of the circuit.

{"backgroundColor":"#ffffff","id":"99","type":"$$","aid":null,"backgroundColorModified":false,"code":"$$\\cos \\phi=\\,\\frac{R}{{\\sqrt[]{R^{2}\\,+\\,\\omega^{2}L^{2}}}}$$","font":{"size":11,"color":"#000000","family":"Arial"},"ts":1636275680782,"cs":"caxUxXVn+XwT7ZScDJb+sQ==","size":{"width":164,"height":40}}

Since the value of cosΦ is always less than 1 the power dissipation in the L-R circuit is less than that in the pure-resistance circuit for the same voltage and the current.

Wattless Current:- If If the resistance in the a.c. the circuit is zero, although current flows in the circuit, yet the average power remains zero, that is, there is no energy dissipation in the circuit. The current in such a circuit is called wattless current.

Electrical Oscillations in L-C circuit

Electrical Oscillation takes place when a charged capacitor is discharged through an inductor of negligible ohmic resistance. These are known as L-C oscillations. As shown in the figure a capacitor C and resistance-free induction coil L be connected to a battery. Let the switch S be first connected to a to charge the capacitor then to b to discharge the capacitor through the inductance coil L.

When it is fully charged, the charge on the capacitor is q0 then the amount of energy q02/2Cis stored as electrical energy in an electrical field between its plates. At this moment the current in the circuit is zero. (fig a)


1644570446538

When the capacitor is connected to the inductance coil L and starts discharging, an anticlockwise current starts flowing in the circuit(fig b). As the current rises from zero, a magnetic field starts developing around and the inductance L, and when the current reaches its peak value i0 the energy stored as a magnetic field is Li02/2 and the capacitor is entirely discharged. Thus, the electrical energy stored between the plates of the capacitor is transferred to the magnetic field around an inductance. After the capacitor is discharged the current i0 does not become zero suddenly but due to the inductance L continuously flowing in the same direction for the same time while the magnetic field dies down. The current continues to flow in the same direction and the capacitor is again charged in the reverse direction ( fig c). After the capacitor is charged the current becomes zero. The energy stored in the form of a magnetic field is stored in the form of an electric field between the plates of the capacitor.

Now the capacitor discharge in the opposite direction and the current starts in the opposite direction and the current starts increasing from zero in the reverse direction. This process of charging and discharging the capacitor is repeated again and again. According to the current in the L-C-R circuit first rises from zero to a maximum value in one direction, reduced to zero, then rises to the same maximum value in the reverse direction and again reduces to zero. The electrical oscillation occurs in the circuit. The frequency of these oscillations depends upon the capacitance C of the capacitor and the inductance L. It can be shown by calculation that if the resistance of the circuit be negligible, the frequency of the electrical oscillation in the circuit is given by

{"id":"105","backgroundColor":"#ffffff","backgroundColorModified":false,"type":"$$","aid":null,"font":{"color":"#000000","family":"Arial","size":11},"code":"$$f\\,=\\,\\frac{1}{2\\pi}{\\sqrt[]{\\frac{1}{LC}}}\\,=\\,\\frac{1}{2\\pi}{\\sqrt[]{\\frac{1/C}{L}}}$$","ts":1636362834962,"cs":"UvD6hIw0lotb4NTEPu3TjA==","size":{"width":222,"height":41}}

Normally it runs in lacs. These oscillations do not continue for infinite time because there is always some resistance in the circuit due to which some energy is lost in the form of energy.

Transformers

It works on the principle of mutual induction. The transformer is a device that is used for converting a large alternating current at low voltage into a small current at high voltage and vice versa. The transformers that convert low voltage into higher ones are called step-up transformers while those that convert high voltages into lower ones are called step-down transformers

.1644570447124

Construction: A simple transformer consists of two coils called the primary and the secondary, insulated from each other and bound on a common soft iron laminated core. One of the two coils has a smaller number of turns of thick insulated copper wire cover while the other hand a large number of turns of thin insulated copper wire. In a step-up transformer, the coil of the copper wire has a smaller number of turns in a primary coil and the coil of wire has a large number of turns in the secondary coil (fig a) in the step-down transformer the order is reversed.

Theory:- The given source of EMF says AC mains is always connected to the primary coil. When the alternating current flows through the primary coil, then in each cycle of the current, the core is magnetized once in one direction and once in the opposite direction. Moreover, since the secondary coil is also wound on the same core, the magnetic flux passing through it is subjected to continuous changes as the core is magnetized and de-magnetized again and again. Consequently, alternating EMFs at the same frequency are induced in the secondary coil through mutual induction. Depending on the ratio of turns in the two coils, the secondary coil induces its own EMF.

Let Np and Ns be the number of turns in the primary and secondary coil respectively. Let us assume that there is no leakage of magnetic flux so that the same flux passes through each turn of the primary and secondary. Let ΦB be the magnetic flux linked with each turn of either coil at any instant. Then by faraday's law of electromagnetic induction, the EMF induced in the primary coil is given by

{"backgroundColor":"#ffffff","aid":null,"font":{"color":"#000000","family":"Arial","size":11},"code":"$$e_{p}\\,=\\,-\\,N_{p}\\frac{\\Delta \\phi_{B}}{\\Delta t}$$","id":"109","backgroundColorModified":false,"type":"$$","ts":1636364541089,"cs":"TonsOgQYlpjqoIZK0Owmsw==","size":{"width":128,"height":36}}

And the EMF induced in the secondary coil is given by

{"font":{"color":"#000000","family":"Arial","size":11},"aid":null,"code":"$$e_{s}\\,=\\,-\\,N_{s}\\frac{\\Delta \\phi_{B}}{\\Delta t}$$","id":"110","type":"$$","backgroundColorModified":false,"backgroundColor":"#ffffff","ts":1636364635130,"cs":"jYXXo157dAGS+4VGAKsgMQ==","size":{"width":126,"height":36}}

{"code":"$$\\therefore\\,\\,\\,\\,\\,\\frac{e_{s}}{e_{p}}\\,=\\,\\frac{N_{s}}{N_{p}}$$","backgroundColor":"#ffffff","type":"$$","font":{"size":11,"color":"#000000","family":"Arial"},"id":"111","aid":null,"backgroundColorModified":false,"ts":1636364694024,"cs":"ViFdY/9jfF7xZ7WZowIg6g==","size":{"width":106,"height":40}}

The induced EMF ep in the primary coil will be nearly equal to the applied voltage Vp across its ends if there is no resistance in the primary circuit and no loss of energy in it. Likewise, if the secondary circuit is open, then the voltage

VS across its and will equal the EMF es induced in it. Under this condition we have

{"backgroundColorModified":false,"id":"116","font":{"family":"Arial","color":"#000000","size":11},"aid":null,"type":"$$","backgroundColor":"#ffffff","code":"$$\\frac{V_{s}}{V_{p}}\\,=\\,\\frac{e_{s}}{e_{p}}\\,=\\,\\frac{N_{s}}{N_{p}}\\,=\\,r,$$","ts":1636365040499,"cs":"O9Rv7ecEl4hfh4rMBM3tcg==","size":{"width":170,"height":40}}

Where r is called transformer ratio. In a step-up transformer, r is more than 1 whereas in a step-down transformer r is less than 1. Thus,

{"font":{"family":"Arial","color":"#000000","size":11},"type":"$$","backgroundColor":"#ffffff","id":"117","code":"$$\\frac{voltage\\,\\,obtained\\,across\\,\\sec ondary}{voltage\\,applied\\,across\\,primary}\\,=\\,\\frac{no.\\,of\\,turns\\,in\\sec ondary}{no.\\,of\\,turns\\,in\\,primary}$$","aid":null,"backgroundColorModified":false,"ts":1636365401818,"cs":"Kf9HgFxHMEd5Bw60SLe5XQ==","size":{"width":489,"height":38}}

If ip and isbe the current in the primary and the secondary at any instant and the energy losses be zero, then

Power in the secondary = power in the primary

{"code":"\\begin{lalign*}\n&{V_{s}\\times\\,i_{s}\\,=\\,V_{p}\\,\\times\\,i_{p}}\\\\\n&{\\frac{i_{p}}{i_{s}}\\,=\\,\\frac{V_{s}}{V_{p}}\\,=\\,\\frac{N_{s}}{N_{p}}\\,=\\,r}\t\n\\end{lalign*}","font":{"size":11,"color":"#000000","family":"Arial"},"id":"120","type":"lalign*","backgroundColorModified":null,"backgroundColor":"#ffffff","aid":null,"ts":1636365769042,"cs":"Np7nHfC7ANflR2+iyKvROg==","size":{"width":165,"height":61}}

When voltage is stepped-up the current is correspondingly reduced in the same ratio and vice-versa. Thus the energy obtained from the secondary coil is equal to the energy given to the primary coil.


Significance of NCERT class 12 physics chapter 7 notes

Comprehensive Revision: NCERT Alternating Current class 12 notes are an excellent resource for thoroughly reviewing the chapter.

Understanding Main Topics: These notes help you understand the primary topics covered in the chapter, such as voltage applied to a resistor, resistor representation of AC current, and transformer principles.

CBSE Syllabus Coverage: The class 12 physics chapter 7 notes make it easier to cover the essential topics outlined in the CBSE Class 12 Physics Syllabus, which are closely aligned with the curriculum.

Preparation for Competitive Exam: These cbse class 12 physics ch 7 notes not only help students with school exams, but also prepare them for various competitive tests such as VITEEE, BITSAT, JEE MAIN, NEET, and so on.

Offline Preparation Convenience: By downloading the physics class 12 chapter 7 notes pdf format, students can study whenever and wherever they want, according to their schedule.

NCERT Class 12 Notes Chapterwise

Subject Wise NCERT Exemplar Solutions

Subject Wise NCERT Solutions

NCERT Books and Syllabus

Frequently Asked Question (FAQs)

1. Is Alternating Current class 12th notes important for JEE?

Yes, understanding Alternating Current (AC) class 12th notes is important for JEE preparation as it aligns with the syllabus and provides essential knowledge for tackling physics questions in the exam.

2. What are the main derivations included in the NCERT Class 12 Physics chapter 7?

The main derivations covered in the NCERT book are Circuit containing Capacitance and resistance, Circuit containing inductance and capacitance, and Circuit containing Inductance, Capacitance, and resistance in series

3. In what way does the chapter contribute to the CBSE board exam?

It is one of the important chapters, can expect 4 to 6 marks questions from the chapter alternating Current.

4. What are the main topics covered in alternating current Class 12 notes?

There are some major topics covered in alternating current Class 12 notes, including The Application of AC Voltage to a Resistor, Representating AC Current, and Voltage by Rotating Vectors - Phasors, The Application of AC Voltage to an Inductor, The Application of AC Voltage to a Capacitor, The Application of AC Voltage to a Series LCR Circuit, The Application of AC Voltage to an LCR Circuit, and Power in AC Circuit: The Power Factor

5. Define the transformer according to Alternating Current Class 12 Physics chapter 7 notes.

The transformer is a device that is used for converting a large alternating current at low voltage into a small current at high voltage and vice versa.

These topics can also be downloaded from Alternating Current Class 12 notes pdf download.

Articles

Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

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Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

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K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

3 Jobs Available
Finance Executive
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
Stock Analyst

Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.

2 Jobs Available
Researcher

A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

2 Jobs Available
Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
Conservation Architect

A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

2 Jobs Available
Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software. 

2 Jobs Available
Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials. 

2 Jobs Available
Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
Veterinary Doctor
5 Jobs Available
Speech Therapist
4 Jobs Available
Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

4 Jobs Available
Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
Anatomist

Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.

2 Jobs Available
Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

4 Jobs Available
Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Reporter

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.  

2 Jobs Available
Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Production Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software. 

2 Jobs Available
Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
QA Manager
4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
ITSM Manager
3 Jobs Available
Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process. 

2 Jobs Available
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