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An alternating voltage is given by: `e = e_(1) sin omega t + e_(2) cos omega t`. Then the root mean square value of voltage is given by:A. `sqrt(e_(1)^(2) + e_(2)^(2))`B. `sqrt(e_(1)e_(2))`C. `sqrt((e_(1)e_(2))/(2))`D. `sqrt((e_(1)^(2) e_(2)^(2))/(2))` |
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Answer» Correct Answer - D `e = e_(1) sin omega t + e_(2) cos omega t` `= sqrt(e_(1)^(2) + e_(2)^(2)) [sin omega t (e_(1))/(sqrt(e_(1)^(2) + e_(2)^(2))) + cos omega t (e_(2))/(sqrt(e_(1)^(2) + e_(2)^(2)))]` `implies sqrt(e_(1)^(2) + e_(2)^(2)) [sin omega t cos phi + cos omega t sin phi]` `implies e = sqrt(e_(1)^(2) + e_(2)^(2)) sin (omega t + phi)` where `phi = "tan"^(-1) (e_(2))/(e_(1))` `e_("rms") = (e_("max"))/(sqrt(2)) = sqrt(e_(1)^(2) + e_(2)^(2))/(sqrt(2)) = sqrt((e_(1)^(2) + e_(2)^(2))/(2))` |
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