Question

An input voltage represented by waveform as shown below is applied to a true RMS meter. The reading of instrument will be_____V.(upto two decimal places)

• A. 2.18

Answer 1

The correct option is A 2.18
Input waveform shown above is periodic waveform with time period of 2$\pi$.
The true rms meter shows rms value,

$V_{rms\left(meter\right)}=\sqrt{\frac{1}{T_0}\left[{\int }_0^{T_0}{V}^2\right(t\left)dt\right]}$

$V_{rms\left(meter\right)}=\sqrt{\frac{1}{2\pi }\left[{\int }_0^{\pi /2}\right(4{)}^{2}dt+{\int }_{\pi /2}^{2\pi }(-1{)}^{2}dt]}$

$=\sqrt{\frac{1}{2\pi }[16(\frac{\pi }{2}-0)+1(2\pi -\frac{\pi }{2})]}$

$=\sqrt{\frac{1}{2\pi }[8\pi +\frac{3\pi }{2}]}=\sqrt{\frac{1}{2\pi }.\frac{19\pi }{2}}$

$=\sqrt{\frac{19}{4}}=2.179\simeq 2.18V$