Calculate the reading which will be given by a hot-wire voltmeter if it is connected across the terminals of generator whose voltage waveform is represented by
`v = 200 sin omega t + 100 sin 3 omega t + 50 sin omega t`

Options

A. `110 V`
B. `162 V`
C. `200 V`
D. `220 V`

Answer

B

Explanation

Since hot wire voltmeter reads only rms value we will have to find rms value of the given voltage. Considering one complete cycle,
`v_("rms") = sqrt((1)/(2 pi) int_(0)^(2 pi) v^(2) d theta)`
`v_("rms") (1)/(2 pi) int_(0)^(2 x) (200 sin theta + 100 sin 3 theta + 50 sin 5 theta)^(2) d theta`
`= (1)/(2 pi) int_(0)^(2pi) (200 sin theta + 100 sin 3 theta + 50^(2) sin^(2) 5 theta)^(2)`
`+ 2 xx 200 xx 100 sin theta sin 3 theta`
`+ 2 xx 100 xx 50 sin 3 theta sin 5 theta`
`+ 2 xx 50 + 200 sin 5 theta sin theta) d theta`
`= (1)/(2 pi) ((200^(2))/(2) + (100^(2))/(2) + (50^(2))/(2)) 2 pi = 26,250`
`v_("rms") = sqrt(2650) = 162 V`