A) \[\frac{E_{0}^{2}}{R}\]
B) \[\frac{E_{0}^{2}}{2R}\]
C) \[\frac{E_{0}^{2}}{4R}\]
D) \[\frac{E_{0}^{2}}{8R}\]
Correct Answer: C
Solution :
\[P={{E}_{rms}}{{i}_{rms}}\cos \varphi =\frac{{{E}_{0}}}{\sqrt{2}}\times \frac{{{i}_{0}}}{\sqrt{2}}\times \frac{R}{Z}\] Þ \[\frac{{{E}_{0}}}{\sqrt{2}}\times \frac{{{E}_{0}}}{Z\sqrt{2}}\times \frac{R}{Z}\]\[\Rightarrow \,\,P=\frac{E_{0}^{2}R}{2{{Z}^{2}}}\] Given \[{{X}_{L}}=R\] so, \[Z=\sqrt{2}R\]\[\Rightarrow \,P=\frac{E_{0}^{2}}{4R}\]
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