CAIE A-Level Physics 21.1.3 Mean Power in a Resistive A.C. Load

Practise relating maximum and mean power in a resistive circuit with sinusoidal current, including the factor of one half.

Exam points

calculate mean power in a resistive load as half the maximum power for a sinusoidal current
compare maximum and mean power and apply the relationship in a resistive circuit

[Maximum number: 2]

The output voltage V of an a.c. power supply varies sinusoidally with time t as shown in Fig. 7.2.

Fig. 7.2

The supply is connected to a $12 \Omega$ resistor. Calculate the mean power dissipated in the resistor.
mean power =
W

$(\mathrm{P}=) \frac{\mathrm{V}^{2}}{2 \mathrm{R}} \text { or }(\mathrm{P}=) \frac{V_{\text {r.m.s. }}{ }^{2}}{\mathrm{R}}$ $=\frac{3.5^{2}}{2 \times 12}$ or $\frac{2.47^{2}}{12}$

C1

$=0.51 \mathrm{~W}$

A1

All question bank results loaded

21.1.3—The fact that the mean power in a resistive load is half the maximum power question 1