Question

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

विकल्प

• `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 ωt 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 sine wave cycle, the positive and negative halves exhibit symmetry with respect to the time axis. The positive area above the axis is equal in magnitude to the negative area below it, resulting in their cancellation. Hence, the average value over the complete cycle becomes zero.

V_avg = 0

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