A) \[\frac{50}{\sqrt{2}},0\]
B) \[50,\,\,0\]
C) \[50,\,\,10\]
D) \[\frac{1000}{\sqrt{2}},\,\,10\]
Correct Answer: D
Solution :
\[e=100\sin (30t)\] \[i=20\sin \left( 30t-\frac{\pi }{4} \right)\] \[{{e}_{rms}}=\frac{100}{\sqrt{2}}volt,\] \[{{i}_{rms}}=\frac{20}{\sqrt{2}}amp\] Power factor \[=\cos \phi =cos\left( -\frac{\pi }{4} \right)=\frac{1}{\sqrt{2}}\] \[<P>={{e}_{rms}}{{i}_{rms}}\cos \phi \] \[=\frac{100}{\sqrt{2}}\times \frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}\] \[=\frac{1000}{\sqrt{2}}watt\] Wattles current\[={{i}_{rms}}\sin \phi \] \[=\frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=10amp\]
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