Question

An alternating voltage varies with time (t) as V = 100 sin (50 πt). The rms voltage and the frequency respectively, are ______.

Options

• `100/sqrt2` V, 50 Hz

• 100 V, 25 Hz

• 100 `sqrt2` V, 50 Hz

• `100/sqrt2` V, 25 Hz

Answer 1

An alternating voltage varies with time (t) as V = 100 sin (50 πt). The rms voltage and the frequency respectively, are `bbunderline(100/sqrt2 "V", 25 "Hz")`.

Explanation:

V = 100 sin (50πt)

V = V0 sin (ωt)

V₀ = 100 v, ω = 50π

V_rms = `"V"_0/sqrt"z"`

V_rms = `100/sqrt"2"`

ω = 2πf

f = `omega/(2pi)=(50pi)/(2pi)`

f = 25 Hz