An A.C. is given by equation (I = I\_1\cos,\omega t + I\_2,\... | Physics | SolveeIt | Solveeit

Today, August 20

Question

An A.C. is given by equation $I = I_1\cos\,\omega t + I_2\,\sin \,\omega t$ . The r.m.s. value of current is given by

A

$\frac{I_1+I_2}{2}$

B

$\frac{(I_1+I_2)^2}{\sqrt2}$

C

$\frac{1}{\sqrt2}\sqrt{I^2_1+I^2_2}$

D

$\frac{I^2_1+I^2_2}{2}$

Answer

$\frac{1}{\sqrt2}\sqrt{I^2_1+I^2_2}$

Explanation

Solution

$I=I_1\,\cos\,\omega t+I_2\,\sin\,\omega t+2I_1I_2\,\cos\,\omega\,t .\sin \,\omega t$ $I^2_1.\frac{1}{2}I^2_2.\frac{1}{2}+2I_1I_2\times 0; I_{rms}=\frac{(I^2_1+I^2_2)^{1/2}}{\sqrt{2}}$