Question

The rms and the average value of an ac voltage \[ V=V_0\sin\omega t \] over a cycle respectively will be:

• A. \(\dfrac{V_0}{2},\dfrac{V_0}{2}\)
• B. \(\dfrac{V_0}{\pi},\dfrac{V_0}{2}\)
• C. \(\dfrac{V_0}{\sqrt{2}},0\)
• D. \(V_0,\dfrac{V_0}{2}\)

Hint:

For a sinusoidal AC quantity: \[ V_{\text{rms}}=\frac{V_0}{\sqrt2} \] \[ I_{\text{rms}}=\frac{I_0}{\sqrt2} \] and the average value over one complete cycle is always \[ 0. \] Do not confuse this with the average value over only one half-cycle, which is \(\frac{2V_0}{\pi}\).

Answer 1

The Correct Option is C