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InterviewSolution
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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`A. `110 V`B. `162 V`C. `200 V`D. `220 V` |
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Answer» Correct Answer - B 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` |
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