Electricity
Electricity tests direct-current circuit analysis: Ohm's law, resistivity, series and parallel networks, EMF and internal resistance, power and potential dividers, with Kirchhoff's laws as the underlying rules.
Circuit rules
Current I = Q/t. Ohm's law V = IR holds for a component at constant temperature. Resistance of a uniform wire is R = ρL/A, so doubling the length doubles R and doubling the diameter quarters it. In series the current is the same and resistances add; in parallel the p.d. is the same and 1/R = 1/R₁ + 1/R₂.
EMF and power
A real cell has EMF ε and internal resistance r: ε = I(R + r), and terminal p.d. V = ε − Ir. Power P = VI = I²R = V²/R. A potential divider gives V_out = V_in × R₂/(R₁ + R₂) for the resistor across the output. Kirchhoff: the sum of currents at a junction is zero; the sum of EMFs equals the sum of p.d.s around a loop.
Worked example
A cell of EMF 6.0 V and internal resistance 0.50 Ω is connected to a 2.5 Ω resistor. Total resistance = 3.0 Ω, so I = 6.0/3.0 = 2.0 A. Terminal p.d. = 6.0 − (2.0 × 0.50) = 5.0 V. Power in the external resistor = I²R = 2.0² × 2.5 = 10 W; power wasted internally = 2.0² × 0.50 = 2.0 W; total = 12 W, which matches εI.
Traps
Ignoring internal resistance when a question specifies a real cell; using the EMF instead of the terminal p.d. in V²/R; adding parallel resistors directly; assuming current is used up around a circuit; mishandling reciprocal sums on a calculator.