The RMS value of a sinusoidally varying waveform is 5√2. If it is

SOLUTION

Concept:

A general AC sinusoidal wave is expressed as:

v(t) = Vm sin (ωt)

Vm = Peak Value

ω = Angular frequency

RMS value 'or' the effective value of an alternating quantity is calculated as:

\({V_{rms}} = \sqrt{\frac{1}{T}\mathop \smallint \limits_0^T {v^2}\left( t \right)dt} \)

T = Time period

Calculation:

Given Vrms = 5√2

For a sinusoidally varying waveform, the RMS value is given by:

\(V_{rms}=\frac{V_m}{√2}\)

Vm = √2 × Vrms

Vm = √2 × 5√2 = 10

The waveform will be represented as:

V = Vm sin 2 πft

V  =10 sin 2.π.50t

V = 10 sin 100 πt