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Question:

An $\mathrm{AC}$ current is given by $\mathrm{I}=\mathrm{I}_{1} \sin \omega \mathrm{t}+\mathrm{I}_{2} \cos \omega \mathrm{t}$.

A hot wire ammeter will give a reading :

  1. (1) $\sqrt{\frac{\frac{I_{1}^{2}-I_{2}^{2}}{2}}{1}}$

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

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

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


Correct Option: 2,

Solution:

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

$\therefore I_{0}=\sqrt{I_{1}^{2}+I_{2}^{2}}$

$\therefore I_{r m s}=\frac{I_{0}}{\sqrt{2}}=\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}$

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