Question

An alternating current is given by i = i₁coswt + i₂sinwt.

Thus rms current is given by

• A. $\frac{i_{1} + i_{2}}{\sqrt{2}}$
• B. $\frac{|i_{1} + i_{2}|}{\sqrt{2}}$
• C. $\sqrt{\frac{i_{1}^{2} + i_{2}^{2}}{2}}$
• D. $\sqrt{\frac{i_{1}^{2} + i_{2}^{2}}{\sqrt{2}}}$

Answer 1

Answer: (C)

$\sqrt{\frac{i_{1}^{2} + i_{2}^{2}}{2}}$

Answer 2

I_rms = {< I² >}^1/2

= { < I₁² cos²wt + I₂² sin²wt + I₁I₂sin²wt >}^1/2

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