A) \[\frac{{{\left( {{I}_{1}}+{{I}_{2}} \right)}^{2}}}{2}\]
B) \[\frac{\left( {{I}_{1}}+{{I}_{2}} \right)}{\sqrt{2}}\]
C) \[\sqrt{\frac{\left( I_{1}^{2}+I_{2}^{2} \right)}{2}}\]
D) \[\frac{\sqrt{I_{1}^{2}-I_{2}^{2}}}{2}\]
Correct Answer: C
Solution :
As, \[I={{I}_{1}}\cos \,\omega t+{{I}_{2}}\sin \,\,\omega t\] \[\therefore \,\,Resultant current, {{I}_{0}} = \sqrt{I_{1}^{2}\,\,+\,\,I_{2}^{2}}\] Hence, the rms current form relation is given by \[{{I}_{rms}}=\frac{{{Z}_{0}}}{\sqrt{2}}=\frac{\sqrt{I_{1}^{2}+I_{2}^{2}}}{\sqrt{2}}\,\,=\,\,\sqrt{\frac{\,I_{1}^{2}+I_{2}^{2}}{2}}\]
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