An alternating emf applied across a purely resistive load is given by

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

v = V_0 \sin \omega t

, and the resulting current is

i = I_0 \sin \omega t

. Attempt all parts: (a) Write the expression for the instantaneous power

p(t)

supplied to the resistor in terms of

V_0

I_0

and

\omega t

. (b) Show, by integrating

p(t)

over one complete cycle, that the average power

\langle P \rangle

supplied to the resistor is

\dfrac{V_0 I_0}{2}

. (c) Given

V_0 = 311\,\text{V}

(which corresponds to an rms value of 220 V) and

I_0 = 5.0\,\text{A}

, calculate the average power delivered to the resistor. (d) If the amplitude of the applied voltage is doubled while the resistance of the load remains unchanged, by what factor will the average power change? Justify your answer.

Related theory

AC Fundamentals
Power in AC Circuits
AC Circuit Analysis
Power in AC circuits and power factor
Alternating Current

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