Question

An ac voltage is given as v = 14 sin(314 t) V. The average and the effective value of the voltage (in V) over a cycle are respectively ______.

Options

• 14 and 7

• 10 and 14

• 0 and 10

• 10 and 0

Answer 1

An ac voltage is given as v = 14 sin(314 t) V. The average and the effective value of the voltage (in V) over a cycle are respectively 0 and 10.

Explanation:

For a purely sinusoidal alternating voltage, the average value over a complete cycle is zero because the positive half-cycle exactly cancels the negative half-cycle.

The effective value is the Root Mean Square (RMS) value.

V_avg (full cycle) = 0

V_rms = `V_0/sqrt 2`

Where V₀ is the peak voltage.

The given equation is v = 14 sin(314 t).

By comparison with v = V₀ sin(ω t),

we find V₀ = 14 V.

The average value over a full cycle is V_avg = 0.

The effective (RMS) value is:

V_rms = `14/sqrt 2`

≈ `14/1.414`

≈ 9.9

≈ 10 V

∴ The values are 0 V and 10 V, respectively.