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Question

(B) The power consumed in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\phi$ is the phase difference between voltage and current

Vedclass · Accepted Answer

$\frac{\pi}{3} \ rad$

Vedclass · Answer

(B) The power consumed in an $AC$ circuit is given by $P = V_{rms} I_{rms} \cos \phi$,where $\phi$ is the phase difference between voltage and current.Maximum power $P_{max}$ occurs when $\cos \phi = 1$,so $P_{max} = V_{rms} I_{rms}$.Given that the lamp consumes $50 \%$ of the maximum power:$P = 0.5 	imes P_{max}$$V_{rms} I_{rms} \cos \phi = 0.5 	imes V_{rms} I_{rms}$$\cos \phi = 0.5 = \frac{1}{2}$$\phi = \cos^{-1}(\frac{1}{2}) = \frac{\pi}{3} \ rad$.

$A$ lamp consumes only $50 \%$ of maximum power in an $AC$ circuit. What is the phase difference between the applied voltage and the circuit current?

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