An AC current is given


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 :

  1. $\sqrt{\frac{\mathrm{I}_{1}^{2}-\mathrm{I}_{2}^{2}}{2}}$

  2. $\sqrt{\frac{\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}}{2}}$

  3. $\frac{\mathrm{I}_{1}+\mathrm{I}_{2}}{\sqrt{2}}$

  4. $\frac{\mathrm{I}_{1}+\mathrm{I}_{2}}{2 \sqrt{2}}$

Correct Option: , 2


$I=I_{1} \sin \omega t+I_{2} \cos \omega t$

$\therefore \mathrm{I}_{0}=\sqrt{\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}}$

$\therefore \mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_{0}}{\sqrt{2}}=\sqrt{\frac{\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}}{2}}$

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