Key Equations

Transformers — AQA A-Level Physics

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Transformer equation
$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$
  • Where:
    • $V_s$ = secondary (output) voltage (V)
    • $V_p$ = primary (input) voltage (V)
    • $N_s$ = number of turns on secondary coil
    • $N_p$ = number of turns on primary coil
Assumes ideal transformer. Step-up: Ns > Np. Step-down: Ns < Np.
Power conservation (ideal transformer)
$$V_p I_p = V_s I_s$$
  • Where:
    • $V_p$ = primary voltage (V)
    • $I_p$ = primary current (A)
    • $V_s$ = secondary voltage (V)
    • $I_s$ = secondary current (A)
Only valid for an ideal (100% efficient) transformer. If voltage increases, current decreases by the same factor.
Power loss in transmission cables
$$P_{\text{loss}} = I^2 R$$
  • Where:
    • $P_loss$ = power dissipated in cables (W)
    • $I$ = current in cables (A)
    • $R$ = total resistance of cables (ohm)
Combined with P = IV to give P_loss = P²R/V², showing losses are proportional to 1/V². This is why the National Grid uses high voltage.
Transmission loss in terms of voltage
$$P_{\text{loss}} = \frac{P^2 R}{V^2}$$
  • Where:
    • $P_loss$ = power dissipated in cables (W)
    • $P$ = power being transmitted (W)
    • $R$ = total resistance of cables (ohm)
    • $V$ = transmission voltage (V)
Derived from P_loss = I²R and I = P/V. Shows that doubling the transmission voltage quarters the power loss.
Transformer efficiency
$$\text{Efficiency} = \frac{V_s I_s}{V_p I_p} \times 100\%$$
  • Where:
    • $V_s I_s$ = output power (W)
    • $V_p I_p$ = input power (W)
Always less than 100% for real transformers. Rearrange to find output: VsIs = (efficiency/100) x VpIp.
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