Current Electricity
What is examined
Current Electricity covers drift velocity, Ohm's law and resistivity, temperature dependence, emf and internal resistance, Kirchhoff's rules, the Wheatstone bridge and the potentiometer. Numericals on drift speed, terminal voltage and bridge balance are common.
Core rules
- Current I = nAev_d, so v_d = I/(nAe). Drift speed is of order 10⁻⁴ m s⁻¹ although the signal travels near light speed.
- R = ρL/A; ρ = m/(ne²τ). Metals: ρ rises with temperature, ρ = ρ₀(1 + αΔT). Semiconductors have negative α.
- Cell: terminal voltage V = ε − Ir on discharge; V = ε + Ir on charging. Series cells add emf and internal resistance.
- Kirchhoff: junction rule ΣI = 0 (charge conservation); loop rule ΣΔV = 0 (energy conservation).
- Wheatstone balance: P/Q = R/S, galvanometer reads zero.
- Potentiometer compares emf with no current drawn at balance: ε₁/ε₂ = l₁/l₂.
Worked example
A copper wire of area 1.0×10⁻⁶ m² carries 1.5 A. With n = 8.5×10²⁸ m⁻³, find v_d. v_d = I/(nAe) = 1.5/(8.5×10²⁸ × 1.0×10⁻⁶ × 1.6×10⁻¹⁹) = 1.5/(1.36×10⁴) ≈ 1.1×10⁻⁴ m s⁻¹. Reasoning: keep all quantities in SI; e = 1.6×10⁻¹⁹ C; the answer confirms that electrons drift slowly.
Traps
Writing R = ρA/L; using V = ε + Ir for discharge; confusing emf with terminal voltage; putting an ammeter in parallel; and forgetting that at potentiometer balance no current is drawn from the cell, so it measures emf, not terminal voltage.