Current Electricity
Current Electricity covers charge flow in conductors: drift velocity, Ohm's law, resistivity, combinations of resistors and cells, Kirchhoff's rules, the Wheatstone bridge and the potentiometer. Papers regularly set a potentiometer or meter-bridge numerical plus a short derivation.
Core rules
- Current I = nAev_d, so v_d = I/(nAe). Drift speed is only millimetres per second even though the signal travels near light speed. Mobility μ = v_d/E.
- Ohm's law V = IR holds for ohmic conductors at constant temperature. R = ρl/A: resistivity is a material property, resistance is not.
- For metals ρ rises with temperature, ρ = ρ₀(1 + αΔT); for semiconductors and carbon it falls. Manganin and constantan have very small α, hence their use in standard resistors.
- A cell of emf ε and internal resistance r gives V = ε − Ir on discharge and I = ε/(R + r) in a simple circuit.
- Kirchhoff: junction rule is charge conservation, loop rule is energy conservation. Fix a sign convention and keep it.
- Wheatstone bridge balances when P/Q = R/S. A potentiometer compares emfs by a null method, so at balance it draws no current from the cell being measured.
Worked example
A copper wire of cross-section 1.0 mm² carries 1.0 A. With n = 8.5×10²⁸ m⁻³, find the drift speed. v_d = I/(nAe) = 1.0/(8.5×10²⁸ × 1.0×10⁻⁶ × 1.6×10⁻¹⁹) = 7.4×10⁻⁵ m s⁻¹. The arithmetic hinges on converting mm² to 10⁻⁶ m² and on remembering how small drift velocity really is.
Traps
Quoting terminal voltage as emf while current flows; sign slips in Kirchhoff loops; ignoring end corrections in a meter bridge; using a potentiometer whose driver-cell emf is below the emf being measured; and confusing ρ with R when a wire is stretched, where volume is constant so R rises as l².