Question

An alternating current is given by the equation$i = i_{1}\cos\omega t + i_{2}\sin\omega t$. The r.m.s. current is given by

• A. $\frac{1}{\sqrt{2}}(i_{1} + i_{2})$
• B. $\frac{1}{\sqrt{2}}(i_{i} + i_{2})^{2}$
• C. $\frac{1}{\sqrt{2}}(i_{1}^{2} + i_{2}^{2})^{1/2}$
• D. $\frac{1}{2}(i_{1}^{2} + i_{2}^{2})^{1/2}$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2}}(i_{1}^{2} + i_{2}^{2})^{1/2}$

Answer 2

$i_{rms} = \sqrt{\frac{i_{1}^{2} + i_{2}^{2}}{2}} = \frac{1}{\sqrt{2}}(i_{1}^{2} + i_{2}^{2})^{1/2}$