Question

An AC current is given by $I = I _{1} \sin \omega t + I _{2}$ cos$\omega$. A hot wire ammeter will give a reading :

• A. $\sqrt{\frac{I_{1}^{2}-I_{2}^{2}}{2}}$
• B. $\sqrt{\frac{ I _{1}^{2}+ I _{2}^{2}}{2}}$
• C. $\frac{ I _{1}+ I _{2}}{\sqrt{2}}$
• D. $\frac{ I _{1}+ I _{2}}{2 \sqrt{2}}$

Answer 1

Answer: (B)

$I = I _{1} \sin \omega t + I _{2} \cos \omega t$
$\therefore I _{0}=\sqrt{ I _{1}^{2}+ I _{2}^{2}}$
$\therefore I _\,{ rms }=\frac{ I _{0}}{\sqrt{2}}=\sqrt{\frac{ I _{1}^{2}+ I _{2}^{2}}{2}}$