Current Electricity
Current Electricity tests Ohm's law and resistivity, drift velocity and mobility, emf versus terminal voltage, Kirchhoff's laws, the Wheatstone bridge and meter bridge, and the potentiometer. Numericals on internal resistance and bridge balance are common.
Core rules
- I = nAev(d); drift velocity is small (order 10⁻⁴ m/s) although the field propagates near light speed.
- R = ρL/A; resistivity rises with temperature for metals, falls for semiconductors. Mobility μ = v(d)/E.
- Terminal voltage V = ε − Ir on discharge; V = ε + Ir while charging. Maximum power transfer occurs when R = r.
- Kirchhoff: junction rule (charge conservation) and loop rule (energy conservation); fix a sign convention and keep it.
- Wheatstone bridge balances when P/Q = R/S; the meter bridge uses R/S = l/(100 − l).
- Potentiometer: V ∝ l, and at balance no current is drawn from the cell, so it reads true emf. Potential gradient k = V/L.
- Combination rules: series R = ΣR(i), parallel 1/R = Σ1/R(i).
Worked example
A copper wire of cross-section 1.0 mm² carries 1.0 A, with n = 8.5×10²⁸ m⁻³. Then v(d) = I/(nAe) = 1/(8.5×10²⁸ × 1×10⁻⁶ × 1.6×10⁻¹⁹) = 1/(1.36×10⁴) = 7.4×10⁻⁵ m/s. This tiny drift still delivers a large current because the carrier density is enormous.
Traps
- Treating terminal voltage as equal to emf when current flows.
- Reversing a sign in a Kirchhoff loop and losing the whole numerical.
- Using the potentiometer formula with length in centimetres rather than the ratio of lengths.