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 \[e=\frac{1}{\sqrt{2}}\sin (100\pi t+\pi /3)\] |
| \[\therefore \] \[{{i}_{0}}=\frac{1}{\sqrt{2}}\] |
| and \[{{V}_{0}}=\frac{1}{\sqrt{2}}\] |
| We know that average power \[{{P}_{av}}={{V}_{rms}}\times {{i}_{rms}}\cos \phi \] |
| \[=\frac{1}{2}\times \frac{1}{2}\times \cos {{60}^{o}}\] |
| \[\left[ \because {{i}_{rms}}=\frac{{{i}_{0}}}{\sqrt{2}}\text{and}\,{{V}_{rms}}=\frac{{{V}_{0}}}{\sqrt{2}} \right]\] |
| \[=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\]\[=\frac{1}{8}W\] |
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