Is it correct to say: Confusing terminal voltage V with EMF ε when current flows?

V equals ε only for an ideal cell (r = 0) or open circuit (I = 0). Otherwise V = ε - Ir.

Is it correct to say: Writing R = ρA/L instead of ρL/A?

Resistance grows with length, falls with area. Remember: long thin wire → high R.

Is it correct to say: Applying Ohm's law V = IR to non-ohmic devices (diode, thermistor, filament)?

V = IR only for ohmic materials at fixed temperature. For diodes and semiconductors, the V–I graph is non-linear.

Is it correct to say: Missing sign convention in KVL — treating all resistor drops as positive?

Pick a loop direction. If you traverse a resistor along the current, drop is −IR; against current, +IR. EMF: -→+ inside cell is +ε.

Is it correct to say: Assuming drift velocity is high because current flows fast?

v_d is typically 10⁻⁴ m/s (0.1 mm/s). The *signal* travels at nearly c because the field sets up almost instantly.

Is it correct to say: Using resistivity temperature formula ρ_0(1+αΔT) with T in Kelvin vs Celsius inconsistently?

ΔT is a temperature *difference*, so K and °C give the same number. But T_0 must match ρ_0's reference.

Formula sheet (PDF) →

Physics · Chapter 3

Current Electricity

Drift velocity, Ohm's law, Kirchhoff's laws, Wheatstone bridge, cells and internal resistance — NCERT Class 12 Physics Ch 3

13 formulas · 3 solved examples · 6 practice questions · Board weight: 7 marks · CBSE Class 12 · 2025–26 syllabus

Board Exam Tips

→Wheatstone bridge derivation using Kirchhoff's laws is a repeat 3-mark favourite. Practise labelling arms P, Q, R, S consistently.
→Drift velocity derivation of Ohm's law (v_d = eEτ/m) frequently appears as a 3-mark question — memorise the four-step chain.
→Never forget internal resistance r: terminal voltage V = ε - Ir, not ε.
→Units matter: current density J is A/m², resistivity ρ is Ω·m, conductivity σ is S/m. Marks lost for missing units.
→Kirchhoff's laws are always in the exam — practise sign conventions before entering the hall.

Diagram

Cell with internal resistance driving current through an external resistor

Formulas(13)

Electric Current

I = \frac{d q}{d t}

Symbol	Meaning
$I$	Current (A = C/s)
$q$	Charge crossing a section (C)
$t$	Time (s)

Drift Velocity and CurrentBoard favourite

I = n e A v_{d}

Symbol	Meaning
$n$	Free-electron density (m⁻³)
$e$	Electron charge = 1.6×10⁻¹⁹ C
$A$	Cross-sectional area (m²)
$v_{d}$	Drift velocity (m/s)

Drift Velocity in Terms of FieldBoard favourite

v_{d} = \frac{e E τ}{m}

Ohm's Law (microscopic form)

J = σ E, σ = \frac{n e ^{2} τ}{m}

Ohm's Law (macroscopic form)Board favourite

V = I R

Resistance of a Uniform Conductor

R = \frac{ρ L}{A}

Symbol	Meaning
$ρ$	Resistivity (Ω·m)
$L$	Length (m)
$A$	Cross-section area (m²)

Temperature Dependence of Resistivity

ρ_{T} = ρ_{0} [1 + α (T - T_{0})]

Kirchhoff's Junction Rule (KCL)

\sum I_{in} = \sum I_{o u t}

Kirchhoff's Loop Rule (KVL)Board favourite

\sum_{l oo p} ε - \sum_{l oo p} I R = 0

EMF and Terminal Voltage

V = ε - I r

Symbol	Meaning
$ε$	EMF of cell (V)
$r$	Internal resistance (Ω)
$V$	Terminal voltage (V)

Wheatstone Bridge BalanceBoard favourite

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

Cells in Series and Parallel

ε_{e q}^{ser i es} = ε_{1} + ε_{2}, \frac{ε _{e q}}{r _{e q}} = \frac{ε _{1}}{r _{1}} + \frac{ε _{2}}{r _{2}} (p a r a l l e l)

Electric Power

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

Solved Examples

1Solved Exampleeasy4 steps

A copper wire of cross-section 1 mm² carries a current of 1.6 A. If n = 8.5×10²⁸ electrons/m³, find the drift velocity of electrons.

Convert to SI units

A = 1 mm^{2} = 1 0^{- 6} m^{2}, I = 1.6 A

2Solved Exampleboard4 steps

A cell of EMF 2.0 V and internal resistance 0.5 Ω is connected to an external resistor of 4.5 Ω. Find (a) current in the circuit, (b) terminal voltage, (c) power dissipated in the external resistor.

Total resistance in circuit

R_{t o t a l} = R + r = 4.5 + 0.5 = 5.0 Ω

3Solved ExampleHOTS4 steps

In a Wheatstone bridge P = 10 Ω, Q = 15 Ω, R = 20 Ω. Find the value of S for balance. If a 2 V battery of negligible internal resistance is connected, find the current drawn from it.

Apply balance condition

\frac{P}{Q} = \frac{R}{S} \Rightarrow S = \frac{QR}{P} = \frac{15 \times 20}{10} = 30 Ω

Traps & Common Mistakes

Common Mistakes6

1
Confusing terminal voltage V with EMF ε when current flows
✓V equals ε only for an ideal cell (r = 0) or open circuit (I = 0). Otherwise V = ε - Ir.
2
Writing R = ρA/L instead of ρL/A
✓Resistance grows with length, falls with area. Remember: long thin wire → high R.
3
Applying Ohm's law V = IR to non-ohmic devices (diode, thermistor, filament)
✓V = IR only for ohmic materials at fixed temperature. For diodes and semiconductors, the V–I graph is non-linear.
4
Missing sign convention in KVL — treating all resistor drops as positive
✓Pick a loop direction. If you traverse a resistor along the current, drop is −IR; against current, +IR. EMF: -→+ inside cell is +ε.
5
Assuming drift velocity is high because current flows fast
✓v_d is typically 10⁻⁴ m/s (0.1 mm/s). The *signal* travels at nearly c because the field sets up almost instantly.
6
Using resistivity temperature formula ρ_0(1+αΔT) with T in Kelvin vs Celsius inconsistently
✓ΔT is a temperature *difference*, so K and °C give the same number. But T_0 must match ρ_0's reference.

Practice Yourself

Practice Yourself6 questions

Q1
A wire of resistance 4 Ω is stretched to twice its original length. Find its new resistance (volume constant).
Q2
Two resistors 6 Ω and 12 Ω are in parallel. This combination is in series with a 4 Ω resistor. Total resistance?
Q3
A cell of EMF 6 V has internal resistance 1 Ω. When short-circuited, what current flows?
Q4
The resistance of a metal wire is 20 Ω at 20°C and 30 Ω at 120°C. Find its temperature coefficient of resistance.
Q5
In a Wheatstone bridge, if arm resistances are 100, 200, 300 Ω and the fourth arm has an unknown X, find X for balance (arrangement: 100 opposite 300).
Q6
A 100 W bulb and a 60 W bulb both rated 220 V are connected in series across 220 V mains. Which bulb glows brighter?

Notes

Current Electricity — key concepts

Study of electric charge in motion: how it flows through conductors, what resists it, and how circuits with batteries and resistors behave.

Two pictures of Ohm's law

Microscopic: $J = \sigma E$ — current density is proportional to the electric field inside the conductor. Follows from the drift-velocity model ( $v_d = eE\tau/m$ ).
Macroscopic: V = IR — the total voltage across a wire is proportional to the current through it. Same physics, different scale.

Both hold only at constant temperature and only for ohmic materials.

Cell, EMF and internal resistance

EMF ( $\varepsilon$ ): the energy per unit charge supplied by the source when no current flows.
Internal resistance (r): unavoidable resistance inside the cell.
When a current I is drawn, the terminal voltage drops to $V = \varepsilon - Ir$ . When charging, $V = \varepsilon + Ir$ .

Kirchhoff's laws — always applicable

Junction rule (KCL): conservation of charge — $\sum I_{in} = \sum I_{out}$ .
Loop rule (KVL): conservation of energy — $\sum \varepsilon = \sum IR$ around any closed loop.

For multi-loop networks, write one KVL equation per independent loop and one KCL per independent junction.

Wheatstone bridge in one line

Balance ⇔ P/Q = R/S ⇔ no current through galvanometer. This is the basis of the metre-bridge, used to measure an unknown resistance to good precision.

Quick sanity checks

Doubling wire length at constant volume → resistance rises 4× (since A halves too).
Series resistors ⇒ R_{eq} > any single R. Parallel ⇒ R_{eq} < smallest R.
If terminal voltage $V$ < EMF $\varepsilon$ , current is flowing out of the cell (discharge).
1 Ω × 1 A = 1 V. 1 V × 1 A = 1 W. Cross-check units before finalising numerical answers.