Q1. A wire of resistivity 1.7×10⁻⁸ Ω·m, length 2 m and cross-section 1×10⁻⁶ m² is used. Find its resistance.
R = ρL/A
R = (1.7×10⁻⁸ × 2) / (1×10⁻⁶)
R = 3.4×10⁻⁸ / 10⁻⁶ = 0.034 Ω
Current Electricity — Class 12
The chapter that powers half the paper. Use the calculator to feel V = IR and electrical power, then drill EMF and resistivity numericals.
Electric current & drift velocityCurrent I = nAev_d, the slow net drift of electrons (~mm/s) under an applied field. SI unit: ampere (A).
Resistance & resistivityR = ρL/A. Resistivity ρ is a property of the material; it rises with temperature for metals.
EMF & internal resistanceEMF (E) is the full voltage of a cell; terminal voltage V = E − Ir, where r is the internal resistance.
Kirchhoff's lawsJunction rule: ΣI = 0 (charge conserved). Loop rule: ΣV = 0 (energy conserved) around any closed loop.
Ohm's law & power calculator Interactive
Set the voltage and resistance to read the current and power dissipated.
Current, I = V/R—A
Power, P = V²/R—W
Power lost as heat in a wire is I²R — that is why transmission uses high voltage (low current) to cut losses.
Numericals practice Interactive
Ohm's law, power and EMF problems with worked steps.
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Solved numericals
Q2. A battery of EMF 10 V and internal resistance 0.5 Ω drives a current of 2 A. Find the terminal voltage.
V = E − Ir
V = 10 − (2 × 0.5)
V = 10 − 1 = 9 V
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Drift current | I = n A e v_d | ampere (A) |
| Ohm's law | V = I R | — |
| Resistivity | R = ρ L / A | ohm (Ω) |
| EMF & internal resistance | E = I (R + r) | volt (V) |
| Electric power | P = VI = I²R = V²/R | watt (W) |
| Wheatstone balance | P/Q = R/S | — |
Common mistakes & exam wins
- Terminal voltage V = E − Ir is always less than the EMF when current flows (and equals E only on open circuit).
- Resistivity depends on the material and temperature, NOT on the wire's length or thickness.
- Heat produced ∝ I²R, so the thin element heats up, not the thick supply wires.
- In a balanced Wheatstone bridge no current flows through the galvanometer (P/Q = R/S).
Frequently asked questions
What is drift velocity?
The small average velocity (~10⁻⁴ m/s) with which free electrons move through a conductor under an applied electric field, giving I = nAev_d.
What is the difference between EMF and terminal voltage?
EMF is the maximum potential difference of a cell with no current flowing; terminal voltage is the actual voltage across its terminals when current flows, V = E − Ir.
Why does resistance increase with temperature in metals?
Higher temperature means more vigorous lattice vibrations, which scatter the drifting electrons more, raising the resistivity and hence the resistance.
What are Kirchhoff's laws?
The junction rule (sum of currents at a junction is zero — charge conservation) and the loop rule (sum of potential differences around a loop is zero — energy conservation).