Current Electricity
Current electricity tests steady currents, resistance, cells, circuit laws and measuring instruments. Numerical questions usually combine Ohm’s law with power or internal resistance, so keep units in amperes, volts and ohms.
Core rules and concepts
- Current I = Q/t; conventional current is opposite to electron drift. Drift velocity relation: I = neAv_d.
- Resistance R = ρL/A; resistivity ρ depends on material and temperature, not on the wire’s length or area. Metals have positive temperature coefficient; semiconductors usually negative.
- Ohm’s law V = IR applies to ohmic conductors at constant temperature. Kirchhoff’s junction rule conserves charge; loop rule conserves energy.
- For a cell: terminal voltage V = ε − Ir on discharge, where ε is emf and r internal resistance. Power P = VI = I²R = V²/R.
- Wheatstone bridge balance: P/Q = R/S. Potentiometer at balance draws no current and compares emfs directly.
Worked example
A cell of emf 12 V and internal resistance 2 Ω is connected to a 10 Ω resistor. Find current, terminal voltage and efficiency. Total resistance = 12 Ω, so I = 12/12 = 1 A. Terminal voltage = ε − Ir = 12 − (1)(2) = 10 V. External power = I²R = 10 W; internal power = I²r = 2 W. Efficiency = 10/12 = 83.3%.
Traps
- Stretching a wire to twice its length at constant volume quarters its area and makes R four times larger, not twice.
- An ammeter should have low resistance and be in series; a voltmeter should have high resistance and be in parallel.
- Terminal voltage is less than emf only on discharge; on charging it can exceed emf.
- Do not mix resistivity and resistance in temperature-coefficient calculations.