Question

A periodic waveform $f\left(t\right)=(2-3\cos 10t{)}^{2}V$ is given.
Its rms value will be

• A. $3.61V$
• B. $10.80V$
• C. $12.42V$
• D. $77.18V$

Answer 1

The correct option is C $12.42V$

$f\left(t\right)=(2-3\cos 10t{)}^2$ V

$=4+9{\cos }^{2}10t-12\cos 10t$

$=4-12\cos 10t+9\frac{(1+\cos 20t)}{2}$

$=8.5+4.5\cos 20t-12\cos 10t$ V

RMS value, $f_{rms}=\sqrt{\frac{1}{T}{\int }_0^T\left[f\right(t{)}^{2}dt]}=\sqrt{{8.5}^2+\frac{{4.5}^2}{2}+\frac{{12}^2}{2}}$

$=\sqrt{72.25+10.125+72}$

$=\sqrt{154.375}=12.42V$