Alternating Current - Result Question 4
4. The instantaneous values of alternating current and voltages in a circuit are given as
$ \begin{aligned} & i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \text{ amper } \\ & e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \text{ Volt } \end{aligned} $
The average power in Watts consumed in the circuit is :
(a) $\frac{1}{4}$
(b) $\frac{\sqrt{3}}{4}$
(c) $\frac{1}{2}$
(d) $\frac{1}{8}$
[2012M]
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Answer:
Correct Answer: 4. (d)
Solution:
- (d) The average power in the circuit where $\cos \phi=$ power factory
$
=V _{\text{rms }} \times I _{\text{rms }} \cos \phi$
$\phi=\pi / 3=$ phase difference $=\frac{180}{3}=60$
$V _{rms}=\frac{\frac{1}{\sqrt{2}}}{\sqrt{2}}=\frac{1}{2}$ volt
$I _{rms}=\frac{\frac{1}{\sqrt{2}}}{\sqrt{2}}=(\frac{1}{2}) A$
$\cos \phi=\cos \frac{\pi}{3}=\frac{1}{2}$
$
=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}=\frac{1}{8} W$
The instantaneous power is the power in circuit at any instant of time. It is equal to the product of values of alternating voltage and alternating current at that time
$P _{\text{in }}=EI=(E_0 \sin \omega t)(I_0 \sin \omega t)$
(in non-inductive circuit)
$P _{\text{in }}=(E_0 \sin \omega t)(I_0 \sin \omega t \pm \theta)$
(in inductive circuit)
