A) \[\frac{1}{4}\]
B) \[\frac{\sqrt{3}}{4}\]
C) \[\frac{1}{2}\]
D) \[\frac{1}{8}\]
Correct Answer: D
Solution :
Given equations \[i=\frac{1}{\sqrt{2}}\sin (100\pi t)\] and \[e=\frac{1}{\sqrt{2}}\sin (100\pi t+\pi /3)\] \[\therefore \] \[{{\text{i}}_{\text{0}}}=\frac{1}{\sqrt{2}}\text{and}\,{{\text{V}}_{\text{0}}}=\frac{1}{\sqrt{2}}\]. We know that average power \[{{P}_{av}}={{V}_{rms}}\times {{i}_{rms}}\cos \phi \] \[=\frac{1}{2}\times \frac{1}{2}\times \cos {{60}^{o}}\] \[\left[ \because {{i}_{rms}}=\frac{{{i}_{0}}}{\sqrt{2}}and\,{{V}_{rms}}=\frac{{{V}_{0}}}{\sqrt{2}} \right]\] \[=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\] \[\text{=}\frac{\text{1}}{\text{8}}\text{W}\]
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