A) \[\frac{({{I}_{1}}+{{I}_{2}})}{\sqrt{2}}\]
B) \[\frac{{{({{I}_{1}}+{{I}_{2}})}^{2}}}{2}\]
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 A.C. is \[I={{I}_{1}}\cos \omega t+{{I}_{2}}\sin \omega t\] The resultant current is given by \[{{I}_{0}}=\sqrt{I_{1}^{2}+I_{2}^{2}}\] ...(1) Hence, the rms current from relation is \[{{I}_{rms}}=\frac{{{I}_{0}}}{\sqrt{2}}\] \[=\frac{\sqrt{I_{1}^{2}+I_{2}^{2}}}{\sqrt{2}}\] [from eq.(l)] \[=\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}\]
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