Question

An alternating current is given by $i=i_{1}cos\omega t+i_{2}sin\omega t.$ The 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)

$\sqrt{\frac{i_1^2+i_2^2}{2}}$

$i=i_{1}cos\omega t+i_{2}sin\omega t$

Let $i_1=Isin\theta ...\left(1\right)$

$i_2=Icos\theta ...\left(2\right)$

$i=Isin\theta cos\omega t+Icos\theta sin\omega t$

form equation (1) and (2)

$i{{}_1}^2+i{{}_2}^2=I^2(si{n}^2\theta +co{s}^2\theta )$

or $I=\sqrt{i_1^2+i{{}_2}^2}$

$I_{rms}=\frac{I}{\sqrt{2}}=\sqrt{\frac{i_1^2+i_2^2}{2}}$