Question

The root mean square value of alternating current (sine function) is equal to

• A. twice the peak value
• B. half the peak value
• C. $\frac{1}{\sqrt{2}}$ times the peak value
• D. equal to peak value

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}$ times the peak value

$I=I_{0}sin\omega t\Rightarrow {I_{rms}}^2=\frac{{\int }_0^{\frac{2\pi }{\omega }}{\left(I_{0}sin\omega t\right)}^{2}dt}{{\int }_0^{\frac{2\pi }{\omega }}dt}=\frac{I_0^2}{2}\Rightarrow I_{rms}=\frac{I_0}{\sqrt{2}}$