An AC current is given by \(I=I_1\sin\omega t+I_2\cos\omega t\). A hot wire ammeter will give a reading :
Show Hint
- \(\frac{I_1+I_2}{\sqrt{2}}\)
- \(\sqrt{\frac{I_1^2-I_2^2}{2}}\)
- \(\sqrt{\frac{I_1^2+I_2^2}{2}}\)
- \(\frac{I_1+I_2}{2\sqrt{2}}\)
The Correct Option is C
Solution and Explanation
Write \(I=I_1\sin\omega t+I_2\cos\omega t=I_0\sin(\omega t+\phi)\) with \(I_0=\sqrt{I_1^2+I_2^2}\).
\(I_{rms}=\frac{I_0}{\sqrt2}=\sqrt{\frac{I_1^2+I_2^2}{2}}\).
Answer: (3) \(\sqrt{\frac{I_1^2+I_2^2}{2}}\)
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