Question

The rms and the average value of an ac voltage V = V₀ sin ot volt over a cycle respectively will be ______.

Options

• `V_0/2, V_0/sqrt 2`

• `V_0/pi, V_0/2`

• `V_0/sqrt2`, 0

• V₀, `V_0/sqrt 2`

Answer 1

The rms and the average value of an ac voltage V = V₀ sin ot volt over a cycle respectively will be `bbunderline(V_0/sqrt2, 0)`.

Explanation:

For a sinusoidal alternating voltage:

V = V₀ sin ωt

RMS value:

V_rms = `V_0/sqrt 2`

Average value over a complete cycle:

V_avg = 0

The RMS value is defined as:

V_rms = `sqrt(1/T int_0^T V^2 dt)`

For sine wave:

V_rms = `V_0/sqrt 2`

Over one full cycle, the positive half cancels the negative half, and the net average becomes zero.

V_avg = 0

Thus,

(V_rms, V_avg) = `(V_0/sqrt 2, 0)`