NCERT Class 12 Physics Chapter 3 Notes, Current Electricity Class 12 Chapter 3 Notes

Think of plugging in your phone charger. Surge of electric energy starts the operation of your device. The topics that we discussed in Class 12 Physics Chapter 3 Current Electricity has significance in this example as it explains core concepts of current electricity in the real world.

On this particular page, Careers360 has compiled full revision notes for NCERT Chapter 3 Current Electricity, which includes important topics such as Kirchhoff’s Laws, Ohm’s Law and others. These NCERT notes have been prepared by qualified physics faculties using the NCERT textbooks. Advanced simplification techniques have been applied in the notes, making them ideal for quick revisions while retaining and understanding the concepts. No matter what your level is, whether state level boards or CBSE, these notes will guide you during your preparation.

In addition, the Chapter 3 notes for Class 12 Physics have also been provided in PDF format for convenient access so that students can download them and study at their own time.

Also, students can refer,

NCERT Solutions for Class 12 Physics Chapter 3 Current Electricity

NCERT Exemplar Class 12 Physics Chapter 3 Current Electricity

NCERT Class 12 Physics Chapter 3 Notes

Electric Current: The flow of charge through a conductor per unit of time is defined as electric current. It is measured in amperes (A) and is essential for understanding electrical circuits and electromagnetism.

$i=\frac{q}{t}$

Where, i is the current, q is the charge and t is the time.

• If the rate of flow of charge is variable, the current at any time is $i=\frac{dq}{dt}$

Current Density: The amount of electric current flowing through a material per unit cross-sectional area is referred to as its current density. It is a vector quantity denoted by vec J and can be written as,

$\overrightarrow{\mathrm{J}}=\frac{\mathrm{dI}}{\mathrm{dA}}\overrightarrow{\mathrm{n}}$

• If the cross-sectional area is not perpendicular to the current but forms an angle θ with the current direction, then

$\mathrm{J}=\frac{\mathrm{dI}}{\mathrm{dA}\cos \theta }\Rightarrow \mathrm{dI}=\mathrm{JdA}\cos \theta =\overrightarrow{\mathrm{J}}\cdot \mathrm{d}\overrightarrow{\mathrm{A}}\Rightarrow \mathrm{I}=\int \overrightarrow{\mathrm{J}}\cdot \overrightarrow{\mathrm{dA}}$

• Relation between current density and electric field

$\overrightarrow{J}=\sigma \overrightarrow{E}=\frac{\overrightarrow{E}}{\rho }$

Where, σ is conductivity and ρ is resistivity or specific resistance of the substance

Mobility: Mobility for electrons is defined as the drift velocity per unit electric field.

$\mu =\frac{v_d}{E}$

Where, μ is mobility and vd is drift velocity

Ohm’s Law:

Ohm's Law states that in a conductor, under constant external conditions such as temperature and pressure, the current flowing through the conductor is directly proportional to the potential difference across its two ends.

$\begin{array}{rl}& V\propto I\\ & V=IR\end{array}$

R- Electric Resistance

$R=\rho \frac{l}{A}$

where ρ is resistivity / specific resistance, l is the length of the conductor and A is the area of the cross-section of the conductor

• Ohmic Substance: An Ohmic substance is a substance that obeys Ohm's Law. It has a linear I-V graph, and the slope gives the conductance, which is the reciprocal of resistance.
• Non-ohmic Substances: Non-ohmic or non-linear conductors are substances that do not obey Ohm's Law, such as gases and crystal rectifiers.
• Superconductor: Superconductors are materials that have zero resistivity below a critical temperature. Electrical resistance is zero in this state
• In superconductor,s resistivity is zero

,

Resistivity:

$\rho =\frac{m}{n{e}^2\tau }$

Where, m is the mass, n is the number of electrons per unit volume, e is the charge of the electron, and τ is the relaxation time.

• Resistivity is a material's intrinsic property, and its value tends to increase with the presence of impurities and mechanical stress.
• The reciprocal of resistivity is called conductivity.
• The reciprocal of resistance is termed conductance, and its SI unit is either Ω-1 or Siemens.

Temperature-Dependent Resistivity:

$\rho ={\rho }_0(1+\alpha (T-T_0))$

ρ: Resistivity at temperature T

ρo: Resistivity at temperature To

Temperature-Dependent Resistance

• Temperature Coefficient of Resistance

$R_T=R_{T_0}[1+\alpha (T-T_0)]$

RT: Resistance at the temperature T

Ro: Resistance at the temperature To

α: Temperature coefficient of resistance

$\alpha =\frac{R_T-R_0}{R_0(T-T_0)}$

Where the value of α is different at different temperatures

Colour Coding of Resistance:

The carbon resistance typically consists of four coloured ring bands labelled as A, B, C, and D.

• Colour bands A and B indicate the significant digits of the resistance value.
• Colour band C represents the decimal multiplier.
• Colour band D indicates the tolerance, expressed as a percentage, around the specified resistance value.

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Tolerance of Gold is $\pm 5\mathrm{\%}$
Tolerance of Silver is $\pm 10\mathrm{\%}$
Tolerance if no colour $\pm 20\mathrm{\%}$

Grouping of Resistance

Series Grouping of resistanceṁ

$R_{eq}=R_1+R_2+\dots \dots \dots +R_n$

Parallel Grouping of Resistance:

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\dots \dots \dots \dots +\frac{1}{R_n}$

Heat developed in a resistor: When a constant current flows through a resistance R for t seconds, the loss in electric potential energy appears itself as increased thermal energy (heat H) in the resistor. This relationship is expressed mathematically as,

$H=i^{2}Rt$

The power developed $=\frac{\text{ energy }}{\text{ time }}=i^{2}R=iR=\frac{V^2}{R}$ (from Ohm's law)

• The unit of heat is the joule (J), and the unit of power is the watt (W).

Cell: The device which converts Chemical energy into electrical energy is known as an electric cell.

Internal resistance: In the case of a cell the opposition of electrolyte to the flow of current through it. It is shown by r.

• The internal resistance of a cell depends on the distance between electrodes.

$r\propto d$

• The internal resistance of a cell depends on the area of the electrodes

$r\propto A$

• The internal resistance of a cell concentration of electrolyte

$r\propto c$

• The internal resistance of a cell temperature of the electrolyte

$r\propto \frac{1}{\text{ temp }}$

Emf of a cell: The electromotive force (emf) of a cell is defined as the work done or energy carried by unit charge when it completes one full cycle within the circuit.

Potential difference: The potential difference, also known as voltage, is the electrical pressure across the terminals of a cell when it is actively supplying current to an external resistance in the circuit.

Equation of cell

1. When supplying the current: $E=V+iR$
2. When the cell is being charged: $E=V-iR$

Current supplied by the cell:

• Cell supplies a constant current in the circuit.

$i=\frac{E}{R+r}$

Where, R- External resistance and r- internal resistance

• Potential drop inside the cell=ir
• The internal resistance of the cell, $r=(\frac{E}{V}-1)R$
• The power dissipated in external resistance, $P={\left(\frac{E}{R+r}\right)}^{2}R$
• Maximum power is obtained when the resistance value of the load is equal in value to that of the voltage source's internal resistance.

$P_{max}=\frac{E^2}{4r}$

Series grouping of cells:

In series grouping anode of one cell is connected to the cathode of other cells

n- identical cells which are connected in series, then

- Equivalent e.m.f of combination is

$E_{eq}=nE$

- Equivalent internal resistance

$r_{eq}=nr$

- Main current/current from each cell

$i=\frac{nE}{R+nr}$

- The power dissipated in the external circuit is

${\left(\frac{nE}{R+nr}\right)}^2\cdot R$

- Condition for Maximum Power is $\mathrm{R}=\mathrm{nr}$

$P_{max}=n\left(\frac{E^2}{4r}\right)\text{ whennr }\ll R$

Parallel grouping of cells:

In parallel grouping, all anodes are connected to one point and all cathode together at other points

For n cells connected in parallel then,

- Equivalent e.m.f

$E_{eq}=E$

- Equivalent internal resistance

$R_{eq}=\frac{r}{n}$

- The main current is

$=\frac{E}{R+r/n}$

- The potential difference across an external resistance $V=iR$
- Current from each cell $i^{\prime }=i/n$
- The power dissipated in the circuit

$P={\left(\frac{E}{R+r/n}\right)}^{2}R$

- Condition for Maximum Power

$\begin{array}{rl}& R=\frac{r}{n}\\ & P_{max}=n{\left(\frac{E^2}{4r}\right)}_{\text{when }r\gg nR}\end{array}$

Kirchoff's first law: In a circuit, at any junction, the sum of the currents entering the junction must equal the sum of the currents leaving the junction. This law is also known as Junction rule or Kirchoff's current law (KCL)

$\sum i=0$

$i_1+i_3=i_2+i_4$

This law is simply based on the conservation of charge.

Kirchoff's second law: Algebraic sum of all the potential across a closed loop is zero. This law is also known as Kirchhoff's Voltage law (KVL)

This law is based on the conservation of energy.

$\sum V=0$

In closed-loop

$-i_1{R}_1+i_2{R}_2-E_1-i_3{R}_3+E_2+E_3-i_4{R}_4=0$

Potentiometer: A potentiometer is a device that measures potential difference without drawing current from the circuit. It is commonly employed to measure the electromotive force (e.m.f) of a cell accurately and to compare e.m.f values of different cells. Additionally, it is utilized for determining the internal resistance of a given cell.

The potentiometer consists of wires of length 5 to 10 meters arranged on a wooden block as parallel strips of wires with 1-meter length each and ends of wires are joined by thick coppers. The wire has a uniform cross-section and is made up of the same material. A driver circuit that contains a rheostat, key, and a voltage source with internal resistance r. The driver circuit sends a constant current (I) through the wire. The potential across the wire

V=IR

R is proportional to l since area and resistivity are constant. Therefore, V is proportional to length.

$V\propto L$

The secondary circuit contains cell/resistors whose potential is to be measured. Whose one end is connected to a galvanometer and the other end of the galvanometer is connected to a jockey which is moved along the wire to obtain a point where there is no current through the galvanometer. So that So the potential of the secondary circuit is proportional to the length at which there is no current through the galvanometer. This is how the potential of a circuit is measured using the potentiometer

Calibration of potentiometer

In the potentiometer a battery of known emf E. A constant current I is flowing through AB from the driver circuit (that is the circuit above AB). The jockey is slid on potentiometer wire AB to obtain null deflection in the galvanometer. Let l be the length at which the galvanometer shows null deflection. The potential of wire AB (V) is proportional to the length AB(L).

Now

$\begin{array}{rl}& \frac{V}{E}=\frac{L}{l}\\ & V=E\frac{L}{l}\end{array}$

Thus we obtained the potential of wire AB when a constant current is passing through it. This is known as calibration.

Comparison of emf:

$\frac{E_1}{E_2}=\frac{l_1}{l_2}$

Determine the internal resistance of a cell

$\begin{array}{rl}r& =\left(\frac{l_1-l_2}{l_2}\right)R\\ r& =(\frac{E}{V}-1)R\\ \frac{E}{V}& =\frac{l_1}{l_2}\end{array}$

Comparison of resistances:

$\frac{R_2}{R_1}=\frac{l_2-l_1}{l_1}$

Wheatstone's Bridge:

It is an arrangement of four resistances that can be used to measure one of them in terms of rest

$\begin{array}{rl}& \frac{P}{Q}=\frac{R}{S}\\ & V_B=V_D\end{array}$

( Balanced condition )
No current will flow through the galvanometer unbalanced condition: $V_B>V_D$

$(V_A-V_B)<(V_A-V_D)$

Current will flow from A to B

Meter bridge: The meter bridge is used to find the resistance of a wire, enabling the calculation of its specific resistance. Operating on Wheatstone's bridge principle, it provides a precise method for measuring resistance by balancing known and unknown resistances.

$\frac{P}{Q}=\frac{R}{S}\Rightarrow S=\frac{(100-l)}{l}R$

By going through these Class 12 Current Electricity notes, you’ll be well-equipped to tackle exam questions and build a strong grasp of the chapter’s concepts in CBSE Physics. Covering everything from the basics to more complex ideas, these notes ensure that you gain the confidence and knowledge needed to solve problems effectively. Serving as a valuable resource, the Chapter 3 notes help consolidate essential concepts and promote a clearer understanding of the topic—boosting both your preparation and your potential to score high marks in exams.

Importance of NCERT Class 12 Physics Chapter 3 Notes

• The Class 12 Current Electricity notes are very helpful for studying for the CBSE and other state board exams.
• Because it covers over 10% of the final result in the CBSE Class 12 Physics Board Exam, this chapter is important for your overall performance.
• These effectively prepared notes provide a thorough explanation of all important topics while sticking to the CBSE syllabus for Chapter 3.
• Furthermore, these notes are helpful for both board examinations and entrance exam preparation because Chapter 3 is a significant component of competitive exams like JEE Main and NEET.

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