First slide

Power in a.c. circuit

Question

A lamp consumes only 50% of peak power in an a.c. circuit. What is the phase difference between the applied voltage and the circuit current?

Moderate

A

$\frac{π}{6}$
B

$\frac{π}{3}$
C

$\frac{π}{4}$
D

$\frac{π}{2}$

Solution

$P = \frac{1}{2} V_{o} i_{o} cosϕ \Rightarrow P = P_{peak} \cdot cosϕ$
$\Rightarrow \frac{1}{2} (P_{peak}) = P_{peak} cosϕ$
$\Rightarrow cosϕ = \frac{1}{2} \Rightarrow ϕ = \frac{π}{3}$

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