Alternating Current - Result Question 7
7. In an a.c circuit the e.m.f. (e) and the current (i) at any instant are given respectively by
$e=E_0 \sin \omega t$
[2008]
$i=I_0 \sin (\omega t-\phi)$
The average power in the circuit over one cycle of a.c. is
(a) $\frac{E_0 I_0}{2}$
(b) $\frac{E_0 I_0}{2} \sin f$
(c) $\frac{E_0 I_0}{2} \cos f$
(d) $E_0 I_0$
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Answer:
Correct Answer: 7. (c)
Solution:
- (c) The average power in the circuit over one cycle of a.c. is given by
$P _{av}=e _{rms} \times i _{rms} \times \cos \phi$
$=\frac{E_0}{\sqrt{2}} \times \frac{I_0}{\sqrt{2}} \times \cos \phi=\frac{E_0 I_0}{2} \cos \phi$
