A) 200
B) 100
C) 50
D) 25
Correct Answer: D
Solution :
The rate of dissipation of energy in an electrical circuit is called power. The power of an alternating current circuit depends upon the phase difference between the voltage and current, it is given by \[P={{E}_{rms}}\times {{I}_{rms}}\times \cos \phi \] where\[{{E}_{rms}}\]and\[{{I}_{rms}}\]are root mean square value of voltage and current. \[{{E}_{rms}}=\frac{{{E}_{0}}}{\sqrt{2}}=\frac{200}{\sqrt{2}}\] \[{{I}_{rms}}=\frac{{{I}_{0}}}{\sqrt{2}}=\frac{1}{2\sqrt{2}}\] \[\phi =\frac{\pi }{3}\] \[\therefore \] \[P=\frac{200}{\sqrt{2}}\times \frac{1}{2\sqrt{2}}\times \cos \frac{\pi }{3}\] \[\Rightarrow \] \[P=25W\]
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