Key Equations

On Data Sheet

Not on Data Sheet

Electrical power (1)

$$P = IV$$

Kirchhoff's first law

$$\sum I_{\text{in}} = \sum I_{\text{out}}$$

Where:
- $I_in$ = current entering a junction (A)
- $I_out$ = current leaving a junction (A)

Conservation of charge at a junction.

Electrical power (2)

$$P = I^{2}R$$

Kirchhoff's second law

$$\sum \varepsilon = \sum IR$$

Where:
- $\varepsilon$ = e.m.f. of each source (V)
- $I$ = current (A)
- $R$ = resistance of each component (ohm)

Conservation of energy around a closed loop.

Electrical power (3)

$$P = \frac{V^{2}}{R}$$

Where:
- $P$ = power (W)
- $V$ = potential difference (V)
- $R$ = resistance (ohm)

Energy transferred

$$E = IVt$$

Where:
- $E$ = energy (J)
- $I$ = current (A)
- $V$ = potential difference (V)
- $t$ = time (s)

Resistors in series

$$R_{\text{total}} = R_1 + R_2 + R_3$$

Where:
- $R_total$ = total resistance (ohm)
- $R_1, R_2, R_3$ = individual resistances (ohm)

Kilowatt-hour conversion

$$1\;\text{kWh} = 3.6 \times 10^{6}\;\text{J}$$

Resistors in parallel

$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

Where:
- $R_total$ = total resistance (ohm)
- $R_1, R_2, R_3$ = individual resistances (ohm)

Total resistance is always less than the smallest individual resistor. On the AQA data sheet.

Two resistors in parallel (shortcut)

$$R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2}$$

Where:
- $R_total$ = total resistance (ohm)
- $R_1, R_2$ = individual resistances (ohm)

Product over sum. Only works for exactly two resistors.

Potential divider equation

$$V_{\text{out}} = \frac{R_2}{R_1 + R_2} \, V_{\text{in}}$$

Where:
- $V_out$ = output p.d. across R_2 (V)
- $V_in$ = supply p.d. (V)
- $R_1$ = first resistor (ohm)
- $R_2$ = resistor across which V_out is measured (ohm)

Potential divider ratio

$$\frac{V_1}{V_2} = \frac{R_1}{R_2}$$

Where:
- $V_1$ = p.d. across R_1 (V)
- $V_2$ = p.d. across R_2 (V)
- $R_1, R_2$ = series resistances (ohm)

P.d. splits in proportion to resistance.