Electro Magnetic Induction And Alternating Currents Question 94

Question: An alternating current is given by the equation $ i=i_{1}\cos \omega ,t+i_{2}\sin \omega ,t $ . The r.m.s. current is given by [MP PMT 1994]

Options:

A) $ \frac{1}{\sqrt{2}}(i_{1}+i_{2}) $

B) $ \frac{1}{\sqrt{2}}{{(i_{i}+i_{2})}^{2}} $

C) $ \frac{1}{\sqrt{2}}{{(i_{1}^{2}+i_{2}^{2})}^{1/2}} $

D) $ \frac{1}{2}{{(i_{1}^{2}+i_{2}^{2})}^{1/2}} $

Show Answer

Answer:

Correct Answer: C

Solution:

$ i_{rms}=\sqrt{\frac{i_{1}^{2}+i_{2}^{2}}{2}}=\frac{1}{\sqrt{2}}{{(i_{1}^{2}+i_{2}^{2})}^{1/2}} $



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