$$Q = It \qquad V = IR \qquad P = VI = I^2R = \frac{V^2}{R} \qquad E = Pt = VIt$$ $Q$ in coulombs, $I$ in amperes, $V$ in volts, $R$ in ohms, $E$ in joules.

Resistors

$$\text{Series: } R = R_1 + R_2 + R_3 \qquad \text{Parallel: } \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$ For two resistors in parallel: $R = \dfrac{R_1R_2}{R_1 + R_2}$.

• Series: same current, voltages add. Parallel: same voltage, currents add.

Resistivity

$$R = \frac{\rho L}{A} \qquad \text{(resistance increases with length, decreases with cross-sectional area)}$$

Cells

$$E = V + Ir = I(R + r) \qquad V = E - Ir$$ $E$ = e.m.f., $r$ = internal resistance, $V$ = terminal p.d., $R$ = external resistance.

• Cells in series: e.m.f.s add. Identical cells in parallel: e.m.f. is the same as one cell.

Cost of electricity

$$\text{Energy (kWh)} = \text{power (kW)}\times\text{time (h)} \qquad \text{Cost} = \text{units used}\times\text{cost per unit}$$

Fuses

Fuse rating should be slightly above the working current $I = \dfrac{P}{V}$.

Capacitors

$$C = \frac{Q}{V} \qquad E = \tfrac{1}{2}CV^2 \qquad \text{Series: } \frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} \qquad \text{Parallel: } C = C_1 + C_2$$