A) \[\frac{{{I}_{1}}+{{I}_{2}}}{\sqrt{2}}\]
B) \[\frac{|{{I}_{1}}+{{I}_{2}}|}{\sqrt{2}}\]
C) \[\sqrt{\left( \frac{I_{1}^{2}+I_{2}^{2}}{2} \right)}\]
D) \[\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{\sqrt{2}}}\]
Correct Answer: C
Solution :
The equation of AC is \[I={{I}_{1}}\cos \,\omega t+{{I}_{2}}\,\,\sin \,\omega L\] The resultant current is given by \[{{I}_{0}}=\sqrt{I_{1}^{2}+I_{2}^{2}}\] Hence, the rms current from relation is \[{{I}_{rms}}=\frac{{{I}_{0}}}{\sqrt{2}}=\frac{\sqrt{I_{1}^{2}+I_{2}^{2}}}{\sqrt{2}}\] \[=\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}\]
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