Question

If an alternating voltage is represented as E = 141 sin(628 t), then the rms value of the voltage and the frequency are respectively(a) 141V, 628 Hz(b) 100V, 50Hz
(c) 100V,100 Hz(d) 141V, 100 Hz

Answer 1

answer : option (c) 100V, 100Hz

explanation : standard equation of alternating voltage is represented as $E=E_0sin(2\pi\eta t)$ .....(1)

where, $E_0$ is peak voltage and $\eta$ is frequency .

a/c to question,
an alternating voltage is represented as $E=141sin(628)t$......(2)

comparing equations (1) and (2),

$E_0=141V$ and $\eta=\frac{628}{2\pi}$

we know, rms value of voltage is given by, $E_{rms}=\frac{E_0}{\sqrt{2}}$
= 141/√2 ≈ 100V

and frequency = 628/2π = 100Hz