A) \[\frac{({{I}_{1}}+{{I}_{2}})}{\sqrt{2}}\]
B) \[\frac{({{I}_{1}}+{{I}_{2}})}{2}\]
C) \[\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}\]
D) \[\frac{\sqrt{I_{1}^{2}+I_{2}^{2}}}{2}\]
Correct Answer: C
Solution :
The equation of alternating current (AC) is given by \[I={{I}_{1}}\cos \omega \,t+{{I}_{2}}\sin \omega \,t\] The resultant current \[{{I}_{0}}=\sqrt{{{I}_{1}}^{2}+{{I}_{2}}^{2}}\] Also, rms value of current is given by \[{{I}_{rms}}=\frac{{{I}_{0}}}{\sqrt{2}}\] \[\Rightarrow \] \[{{I}_{rms}}=\sqrt{\frac{{{I}_{1}}^{2}+{{I}_{2}}^{2}}{2}}\]
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