By Kumar Sir, Physics faculty at Pramana Institute (IIT Kanpur, 25 years teaching, ex-Allen)
Current electricity is one of the highest-weightage Physics chapters in JEE Main, at about two questions a year by published counts. It also appears regularly in NEET and carries a big share of the Class 12 board paper. Most of its questions are circuits you can solve in under two minutes, if the formulas below are automatic and you avoid three classic traps.
Current and resistance
| Quantity | Formula | Notes |
|---|---|---|
| Current | I = dq/dt = n e A v(d) | n = free electrons per m³, v(d) = drift speed |
| Drift speed | v(d) = eEτ/m | τ = relaxation time |
| Mobility | μ = v(d)/E = eτ/m | SI unit m² V⁻¹ s⁻¹ |
| Ohm's law | V = IR | Ohmic conductors only |
| Resistance | R = ρl/A | ρ = resistivity |
| Resistivity | ρ = m/(n e² τ) | Conductivity σ = 1/ρ |
| Current density | J = I/A = σE | Vector form of Ohm's law |
| Temperature effect | R = R₀(1 + αΔT) | α = temperature coefficient |
| Stretched wire (volume fixed) | R ∝ l², so stretching to n times the length gives n²R | A favourite one-liner |
Combinations and cells
| Quantity | Formula |
|---|---|
| Resistors in series | R = R₁ + R₂ + R₃ + … |
| Resistors in parallel | 1/R = 1/R₁ + 1/R₂ + 1/R₃ + … |
| Terminal voltage (cell discharging) | V = E − Ir |
| Terminal voltage (cell charging) | V = E + Ir |
| Current in a simple circuit | I = E/(R + r) |
| Cells in series | E(eq) = E₁ + E₂, r(eq) = r₁ + r₂ |
| Cells in parallel | E(eq) = (E₁/r₁ + E₂/r₂)/(1/r₁ + 1/r₂), and 1/r(eq) = 1/r₁ + 1/r₂ |
Kirchhoff, bridges and power
| Quantity | Formula |
|---|---|
| Junction rule | ΣI = 0 at any junction |
| Loop rule | ΣΔV = 0 around any closed loop |
| Balanced Wheatstone bridge | P/Q = R/S (no current through the galvanometer) |
| Metre bridge | R/S = l/(100 − l), with l in cm |
| Power | P = VI = I²R = V²/R |
| Heat produced (Joule) | H = I²Rt |
| Maximum power to load | When R = r, P(max) = E²/4r |
Worked examples
1. Stretched wire. A 10 Ω wire is stretched to twice its length. Its volume stays the same, so the area halves and R = 10 × 2² = 40 Ω.
2. Maximum power. A 12 V cell with internal resistance 2 Ω drives a 2 Ω load. I = 12/(2 + 2) = 3 A, so P = 3² × 2 = 18 W. Check: E²/4r = 144/8 = 18 W, the maximum possible from this cell.
Three traps
- Drift speed vs current speed. Drift speed is about 10⁻⁴ m/s, yet a bulb lights instantly because the electric field travels through the wire almost at the speed of light.
- Stretched wires. Length and area change together. Use R ∝ l², not R ∝ l.
- Charging vs discharging. Terminal voltage is E − Ir only when the cell supplies current. When it is being charged, it is E + Ir.
FAQs
Is the potentiometer still in the syllabus? It was removed from the current NCERT book and the JEE Main syllabus. Check the latest notices for NEET and your board. The Wheatstone bridge and Kirchhoff's laws remain.
Which formula is used most in JEE Main? Kirchhoff's laws and series–parallel reduction appear in almost every circuit question.
What is the unit of resistivity? Ohm metre (Ω m).
Solve circuits with weekly tests in a batch of at most 40 at Pramana, Geeta Bhawan Square, Indore. See our IIT JEE and NEET programs, or book free counselling.
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