A) 70.7V.70.7mA
B) 70.7V, 70.7A
C) 141.4V.141.4mA
D) 141.4V, 141.4A
Correct Answer: A
Solution :
The Instantaneous value of voltage is \[\operatorname{E}\,=100\,\,sin\left( 100\,t \right)\,V\] We get \[{{\operatorname{E}}_{0}}=100V,\,\,\omega =\,\,100\,\,rad\,{{s}^{-}}^{1}\] The rms value of voltage is \[{{E}_{rms}}=\frac{{{E}_{0}}}{\sqrt{2}}=\frac{100}{\sqrt{2}}V=70.7\,V\] The instantaneous value of current is \[I=\,\,100\,\,sin\,\left( 100t+\frac{\pi }{3} \right)mA\] Compare it with \[\operatorname{I}={{I}_{0}}\,sin\,(\omega t+\,\,\phi )\] we get \[{{I}_{0}} = 100 mA, \omega \,\,= 100 rad {{s}^{-\,1}}\] The rms value of current is \[{{I}_{rms}}=\frac{{{I}_{0}}}{\sqrt{2}}=\frac{100}{\sqrt{2}}mA=70.7\,mA\]
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