Class 12 · Chapter 3

Current Electricity

Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.

Current Electricity Formula Sheet

10 formulas across 3 topics in Current Electricity.

1 min read

Updated 2026-07-05 · v1.0.0

Ohm's Law & Resistance

Current is drifting charge; resistance opposes it. Ohm's law links the two, and resistivity captures what belongs to the material versus the shape.

I = nAe v(d); v(d) = eEτ/m

Current and drift velocity

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
I	current	A	[A]
n	free electron number density	m⁻³	[L⁻³]
v(d)	drift velocity	m/s	[LT⁻¹]
τ	relaxation time between collisions	s	[T]

Valid when

Drift speed is tiny (~mm/s) yet current flows instantly — the field sets up near light speed

Common mistakes

Current density J = I/A = nev(d) = σE is the local, area-independent quantity

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V = IR

Ohm's law

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
V	potential difference	V	[ML²T⁻³A⁻¹]
I	current	A	[A]
R	resistance	Ω	[ML²T⁻³A⁻²]

Valid when

Holds for ohmic conductors at constant temperature
Non-ohmic: diodes, filaments, electrolytes deviate

Common mistakes

R rises with temperature for metals but FALLS for semiconductors — the sign of the temperature coefficient differs

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R = ρL/A; ρ = m/(ne²τ)

Resistance and resistivity

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
ρ	resistivity of the material	Ω·m	[ML³T⁻³A⁻²]
L	length of the conductor	m	[L]
A	cross-sectional area	m²	[L²]

Valid when

ρ is a material property (independent of shape); R depends on shape too

Common mistakes

Stretching a wire to n times its length makes R go up n² times (length ×n, area ÷n) — a constant-volume trap

Read the concept →

Worth remembering

Temperature dependence: ρ(T) = ρ₀[1 + α(T − T₀)] for metals, α positive and small

Resistor Networks & Kirchhoff's Laws

Series adds resistance, parallel adds conductance. When symmetry fails, Kirchhoff's two laws crack any network.

Series: R(eq) = ΣRᵢ; Parallel: 1/R(eq) = Σ 1/Rᵢ

Resistors in series and parallel

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
R(eq)	equivalent resistance	Ω	[ML²T⁻³A⁻²]

Valid when

Series: same CURRENT; Parallel: same VOLTAGE
Two in parallel: R(eq) = R₁R₂/(R₁ + R₂)

Common mistakes

Parallel equivalent is always SMALLER than the smallest resistor in the group

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KCL: ΣI = 0 at a junction; KVL: ΣV = 0 around a loop

Kirchhoff's laws

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
ΣI	algebraic sum of currents at a node (charge conservation)	A	[A]
ΣV	algebraic sum of EMFs and IR drops around a loop (energy conservation)	V	[ML²T⁻³A⁻¹]

Valid when

KCL = charge conservation; KVL = energy conservation
Assign a consistent sign convention and stick to it

Common mistakes

A negative current from the solution just means the real direction is opposite to your assumed one — the magnitude is still correct

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Balanced when P/Q = R/S (no current through galvanometer)

Wheatstone bridge

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
P, Q, R, S	the four bridge arm resistances	Ω	[ML²T⁻³A⁻²]

Valid when

At balance the galvanometer arm carries NO current, so it can be removed or shorted
Meter bridge and post-office box are practical Wheatstone bridges

Common mistakes

At balance the bridge is independent of the galvanometer resistance and the cell EMF — a favourite conceptual question

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Worth remembering

Balanced-bridge trick: spotting a Wheatstone pattern lets you delete the middle resistor and collapse a scary network instantly

NEET favours symmetry and balanced-bridge shortcuts; JEE Advanced demands full Kirchhoff systems and infinite-ladder networks.

EMF, Cells & Electrical Power

A real cell has internal resistance, so terminal voltage drops under load. Power delivered peaks when the load matches the internal resistance.

V = ε − Ir; I = ε/(R + r)

EMF, internal resistance and terminal voltage

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
ε	electromotive force of the cell	V	[ML²T⁻³A⁻¹]
r	internal resistance	Ω	[ML²T⁻³A⁻²]
V	terminal voltage	V	[ML²T⁻³A⁻¹]

Valid when

Discharging: V = ε − Ir (V < ε); charging: V = ε + Ir (V > ε)
Open circuit (I = 0): V = ε

Common mistakes

Cells in series: EMFs add, internal resistances add; identical cells in parallel: EMF unchanged, r becomes r/n

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P = VI = I²R = V²/R

Electrical power

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
P	power dissipated / delivered	W	[ML²T⁻³]

Valid when

Series (same I): use P = I²R — largest R dissipates most
Parallel (same V): use P = V²/R — smallest R dissipates most

Common mistakes

A bulb rated '100 W, 220 V' has fixed RESISTANCE R = V²/P; its actual power changes if the supply voltage changes

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P(max) when R = r; P(max) = ε²/4r

Maximum power transfer

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Maximising P = ε²R/(R + r)² with respect to R

Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
R	load resistance	Ω	[ML²T⁻³A⁻²]
r	internal (source) resistance	Ω	[ML²T⁻³A⁻²]

Valid when

At maximum power the efficiency is only 50% — half the energy heats the source

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Potentiometer: ε₁/ε₂ = l₁/l₂; Meter bridge: R/S = l/(100 − l)

Potentiometer & meter bridge

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Variables used in this formula, with units and dimensions
Symbol	Meaning	Unit	Dimension
l	balancing length	cm (or m)	[L]

Valid when

Potentiometer draws NO current at balance, so it measures true EMF (unlike a voltmeter)
Potentiometer is more accurate the LONGER the wire (smaller potential gradient)

Common mistakes

A potentiometer compares EMFs or measures internal resistance; it never loads the cell at the balance point

Read the concept →

Worth remembering

Heat produced (Joule's law): H = I²Rt — the basis of fuses, heaters, and the kWh on your electricity bill

NEET repeats terminal-voltage, power-rating and potentiometer questions; JEE Advanced blends max-power-transfer with multi-cell networks.

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Previous chapter2. Electrostatic Potential & Capacitance Next chapter 4. Moving Charges & Magnetism

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