First slide

Alternating current and voltage

Question

An AC is given by equation $I = I_{1} cosωt + I_{2} sinωt$ The r.m.s. value of current is given by

Moderate

A

$\frac{I_{1} + I_{2}}{2}$
B

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

$\frac{1}{\sqrt{2}} \sqrt{I_{1}^{2} + I_{2}^{2}}$
D

$\frac{I_{1}^{2} + I_{2}^{2}}{2}$

Solution

$I = I_{1} cosωt + I_{2} sinωt$
${I^{2}}_{r m s} R = {I^{2}}_{1, r m s} R + {I^{2}}_{2, r m s} R = {(\frac{I_{1}}{\sqrt{2}})}^{2} R + {(\frac{I_{2}}{\sqrt{2}})}^{2} R \Rightarrow I_{r m s} = \sqrt{\frac{{I_{1}}^{2} + {I_{2}}^{2}}{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App