Current Electricity Notes for NEET, Class 12 NCERT

Introduction

Charges in motion form a current. This chapter is about how currents are described, what controls their size, and how circuits behave. Almost every NEET 2027 paper has 2 questions from Current Electricity, the highest of any Physics chapter. Lock down resistor combinations, Kirchhoff's laws, the Wheatstone bridge, EMF with internal resistance, and electrical power.

Electric current

Current I is the rate at which charge flows past a point:

I = \frac{d Q}{d t} .

SI unit: ampere (A) equals 1 C per s. Current is a scalar (despite having a direction): it does not add as a vector at a junction, it adds algebraically.

Conventional current is in the direction of positive charge flow, opposite to the actual direction of electron flow.

Drift velocity and mobility

In a metal, free electrons fly about randomly at very high speeds. When a field is applied, they pick up a small extra drift velocity in the direction opposite to the field. The current:

I = n A e v_{d} .

Here n is the number density of free electrons, A is cross-section, e is electron charge, and v_d is the drift speed. For typical wires, v_d is around 10⁻⁴ m/s, much smaller than the random thermal speed.

Mobility mu equals drift speed per unit field: $v_{d} = μ E$ .

Ohm's law

For most metallic conductors at constant temperature, current is proportional to voltage:

V = I R .

R is called the resistance, in ohms (Ω). Materials that obey this law over a wide range are ohmic; diodes, transistors and gases are non-ohmic (their R varies with V).

Ohm's law: V = I R. Pick the unknown and enter the other two.

V (V)

I (A)

R (Ω)

Voltage V (V)

12.000

V = I R

Resistance and resistivity

Resistance of a uniform conductor depends on its dimensions and material:

R = \frac{ρ L}{A} .

Rho (ρ) is the resistivity (units Ω·m) of the material. Conductivity sigma equals 1/rho. Typical values: copper ≈ 1.7 × 10⁻⁸ Ω·m, iron ≈ 10⁻⁷ Ω·m, silicon ≈ 10³ Ω·m, glass ≈ 10¹⁰ Ω·m.

Resistance is bigger if the wire is longer or thinner. Resistivity rho is the material's contribution.

Selected: Copper, ρ = 1.68e-8 Ω·m

Length L: 1.00 m

Cross-section A: 1.00 mm²

Resistance

16.800 mΩ

R = \frac{ρ L}{A}

Temperature dependence of resistance

For a metal:

R_{T} = R_{0} [1 + α (T - T_{0})] .

Alpha is the temperature coefficient of resistance, typically about 4 × 10⁻³ per K for metals (positive: R increases with T). For semiconductors, alpha is negative: heating produces more carriers, so R drops with T.

Electrical energy and power

Power dissipated in a resistor:

P = V I = I^{2} R = \frac{V ^{2}}{R} .

Energy used over time t equals P × t. Practical unit of energy is the kilowatt-hour: 1 kWh equals 3.6 × 10⁶ J, the energy a 1 kW appliance uses in 1 hour.

Power dissipated by a resistor. NEET often gives bulb wattage and asks for resistance, or gives R and V and asks for P.

Voltage V: 220 V (Indian mains: 220 V)

Resistance R: 484 Ω

Time on: 5 hours

Power

100.0 W

Current I = 0.455 A

Energy used

0.500 kWh

1 kWh costs about ₹6 to ₹8 in India

P = V I = I^{2} R = \frac{V ^{2}}{R}

Series and parallel combinations

Series

Same current through each. Voltages add. Total resistance:

R_{series} = R_{1} + R_{2} + R_{3} + \dots

Parallel

Same voltage across each. Currents add. Reciprocals add:

\frac{1}{R _{parallel}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

Note that this is the OPPOSITE of capacitor combinations. Capacitors and resistors swap rules.

Three resistors. Series: total adds up. Parallel: reciprocals add.

R₁: 2 Ω

R₂: 3 Ω

R₃: 6 Ω

Effective resistance

11.000 Ω

R = R_{1} + R_{2} + R_{3}

EMF and internal resistance

A real cell maintains an EMF (epsilon) plus has internal resistance r. When connected to external R:

I = \frac{ϵ}{R + r}, V_{terminal} = ϵ - I r .

Terminal voltage is less than EMF when current flows. When the cell is being charged externally, terminal voltage exceeds EMF (V = ε + Ir).

Real cell: EMF (epsilon) plus internal resistance (r). When current flows, terminal voltage V drops below the EMF.

EMF ε: 12.0 V

Internal resistance r: 0.50 Ω

External R: 5.0 Ω

Terminal voltage

10.91 V

V = ϵ - I r

2.182 A

P_ext

23.80 W

P_lost (in r)

2.38 W

Combination of cells

Cells in series

EMFs add. Internal resistances add: $ϵ_{eq} = ϵ_{1} + ϵ_{2}, r_{eq} = r_{1} + r_{2}$ .

Cells in parallel (identical)

EMF unchanged. Internal resistance reduces: $r_{eq} = r / n$ for n identical cells.

Practice these on the timed test

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Kirchhoff's laws

Junction rule (KCL)

Sum of currents flowing IN to a junction equals sum of currents flowing OUT:

\sum I_{in} = \sum I_{out} (charge conservation) .

Loop rule (KVL)

Algebraic sum of voltage changes around any closed loop is zero:

loop \sum Δ V = 0 (energy conservation) .

Use these two rules together to solve any DC circuit.

Two cells (ε₁, r₁) and (ε₂, r₂) in parallel driving a common load R. Solved using Kirchhoff's laws.

ε₁: 12 V, r₁: 1.00 Ω

ε₂: 6 V, r₂: 2.00 Ω

Load R: 5.00 Ω

Equivalent cell

ε_eq = 10.000 V, r_eq = 0.667 Ω

I_load

1.765 A

I₁

3.176 A

I₂

-1.412 A

ϵ_{eq} = \frac{ϵ _{1} r _{2} + ϵ _{2} r _{1}}{r _{1} + r _{2}}

Wheatstone bridge

Four resistors P, Q, R, S in a diamond, with a galvanometer between the two midpoints (B and D), and a battery across A and C. The bridge is balanced (no current through the galvanometer) when:

\frac{P}{Q} = \frac{R}{S} .

Used to measure unknown resistance precisely. The balance condition does not depend on the battery voltage or the galvanometer's sensitivity.

Wheatstone bridge with four resistors. The bridge is balanced (no current through the galvanometer) when P/Q = R/S.

P: 10 Ω

Q: 20 Ω

R: 30 Ω

S: 60 Ω

Battery V: 12 V

Bridge state

BALANCED

P/Q = 0.500, R/S = 0.500

V_B − V_D = 0.000 V

Balanced when \frac{P}{Q} = \frac{R}{S}

Meter bridge

A practical version of the Wheatstone bridge. A 1 m wire of uniform resistance per unit length replaces R and S. Find the balance point at length l from one end. Then:

\frac{P}{Q} = \frac{l}{100 - l} .

Worked NEET problems

NEET-style problem · Ohm's law

Question

A wire of resistance

20 Ω

carries a current of

0.5 A

. Find the voltage across it and the power dissipated.

Solution

V = I R = 0.5 \times 20 = 10 V .

P = I^{2} R = 0.25 \times 20 = 5 W .

NEET-style problem · Combinations

Question

Three resistors of 6 Ω, 12 Ω and 12 Ω are connected: the two 12 Ω in parallel, then in series with the 6 Ω. Find the equivalent resistance.

Solution

Two 12 Ω in parallel: $(12 \times 12) / (12 + 12) = 6 Ω$ .

Then in series with 6 Ω: $6 + 6 = 12 Ω$ .

NEET-style problem · EMF and internal r

Question

A cell of EMF 12 V and internal resistance 1 Ω is connected to an external resistance 5 Ω. Find the current and terminal voltage.

Solution

I = \frac{ϵ}{R + r} = \frac{12}{6} = 2 A .

V_{term} = ϵ - I r = 12 - 2 = 10 V .

NEET-style problem · Wheatstone bridge

Question

In a Wheatstone bridge, P = 4 Ω, Q = 8 Ω, R = 6 Ω. Find the value of S for balance.

Solution

\frac{P}{Q} = \frac{R}{S} \Rightarrow S = \frac{QR}{P} = \frac{8 \times 6}{4} = 12 Ω.

NEET-style problem · Power

Question

A 100 W bulb is rated for 220 V. Find its resistance and the current it draws when connected to 220 V.

Solution

R = \frac{V ^{2}}{P} = \frac{22 0 ^{2}}{100} = 484 Ω.

I = \frac{V}{R} = \frac{220}{484} \approx 0.455 A .

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Summary cheat sheet

Current: $I = d Q / d t = n A e v_{d}$ .
Ohm's law: $V = I R$ .
Resistivity: $R = ρ L / A$ .
Temperature (metal): $R_{T} = R_{0} (1 + α Δ T)$ .
Power: $P = V I = I^{2} R = V^{2} / R$ .
Series: $R = R_{1} + R_{2} + \dots$ .
Parallel: $1/ R = 1/ R_{1} + 1/ R_{2} + \dots$ .
EMF + r: $V = ϵ - I r$ , $I = ϵ / (R + r)$ .
KCL: sum of currents at a junction = 0.
KVL: sum of voltage changes around a loop = 0.
Wheatstone: balanced when $P / Q = R / S$ .

Next: try the interactive widgets for Ohm's law, resistor combinations, Kirchhoff and Wheatstone, or work through the 32 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.

Frequently asked questions

How many questions come from Current Electricity in NEET 2027?

You can expect 2 questions from this chapter in NEET 2027. The chapter has the highest PYQ frequency in Physics. Resistor combinations, Kirchhoff's laws, Wheatstone bridge, EMF with internal resistance and electrical power are repeated every year.

What is Ohm's law?

For most metallic conductors at constant temperature, the current I through a conductor is directly proportional to the potential difference V across it. The constant of proportionality is called resistance: V equals I R. Materials that follow this law are called ohmic; semiconductors, gases and vacuum tubes are non-ohmic.

What is drift velocity?

Free electrons in a metal move randomly at high speeds (about 10 to the 5 m per s). When you apply a field, they pick up a tiny additional drift velocity (about a millimetre per second) in the direction opposite to the field. The current is I equals n A e v_d, where n is the number of free electrons per cubic metre, A is cross-section, e is electron charge.

How do resistors combine in series and parallel?

Series: same current through each, voltages add. R_eff equals R_1 plus R_2 plus R_3. Parallel: same voltage across each, currents add. 1 over R_eff equals 1 over R_1 plus 1 over R_2 plus 1 over R_3. Series gives larger total R; parallel gives smaller R, less than the smallest.

What are Kirchhoff's laws?

Two rules for solving circuits. KCL (junction rule): the sum of currents flowing into any junction equals the sum flowing out. This is conservation of charge. KVL (loop rule): the algebraic sum of voltage changes around any closed loop is zero. This is conservation of energy.

What is the Wheatstone bridge balance condition?

A Wheatstone bridge has four resistors P, Q, R and S arranged in a diamond, with a galvanometer between the two midpoints. The bridge is balanced (no current through the galvanometer) when P over Q equals R over S. NEET often gives three of the four resistors and asks for the fourth.

What is the difference between EMF and terminal voltage?

EMF (epsilon) is the voltage of a cell when no current flows: the maximum voltage it can provide. When the cell drives current I through external resistance R, internal resistance r drops some voltage. Terminal voltage V equals epsilon minus I r. So when current flows, V is less than epsilon. When the cell is being charged, V is greater than epsilon.

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Current ElectricityNEET Physics · Class 12 · NCERT Chapter 3

Introduction

Electric current

Drift velocity and mobility

Ohm's law

Resistance and resistivity

Temperature dependence of resistance

Electrical energy and power

Series and parallel combinations

Series

Parallel

EMF and internal resistance

Combination of cells

Cells in series

Cells in parallel (identical)

Kirchhoff's laws

Junction rule (KCL)

Loop rule (KVL)

Wheatstone bridge

Meter bridge

Worked NEET problems

Summary cheat sheet

Frequently asked questions

How many questions come from Current Electricity in NEET 2027?

What is Ohm's law?

What is drift velocity?

How do resistors combine in series and parallel?

What are Kirchhoff's laws?

What is the Wheatstone bridge balance condition?

What is the difference between EMF and terminal voltage?

Continue with the next chapter notes

Track Your NEET Score Across All 90 Chapters