A) \[\text{7}0.\text{7 V},\text{ 7}0.\text{7 mA}\]
B) \[~\text{6}0.\text{9 V},\text{ 69}.\text{3 mA}\]
C) \[~\text{9}0.\text{6 V},\text{ 141}.\text{4 mA}\]
D) \[\text{6}0\text{ V},\text{ 7}0\text{ mA}\]
Correct Answer: A
Solution :
The instantaneous voltage is \[E=100\sin (100t)\text{volt}\] ? (i) Compare it with \[E={{E}_{0}}\sin (\omega t)\]volt We get \[{{\text{E}}_{\text{0}}}\text{=100 volt, }\!\!\omega\!\!\text{ =100 rad }{{\text{s}}^{\text{-1}}}\] The rms value of voltage is \[{{\text{E}}_{\text{rms}}}\text{=}\frac{{{\text{E}}_{\text{0}}}}{\sqrt{\text{2}}}\text{=}\frac{\text{100}}{\sqrt{\text{2}}}\text{volt = 70}\text{.7V}\] The instantaneous value of current is \[\text{I = 100 sin }\left( 100t+\frac{\pi }{3} \right)\text{mA}\] Compare it with \[I={{I}_{0}}\sin (\omega t+\phi )\] We get, \[{{\text{I}}_{\text{0}}}\text{=100 mA, }\!\!\omega\!\!\text{ =100 rad }{{\text{s}}^{\text{-1}}}\] The rms value of current is \[{{\text{I}}_{\text{rms}}}\text{=}\frac{{{\text{I}}_{\text{0}}}}{\sqrt{\text{2}}}\text{=}\frac{\text{100}}{\sqrt{\text{2}}}\text{mA=70}\text{.7mA}\]
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