Question

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_(2)e_(2))`
C. `sqrt(e_(1)e_(2))/(2)`
D. `sqrt(e_(1)^(2)+e_(2)^(2))/(2)`

Answer 1

Correct Answer - D
d) `e=sqrt(e_(1)^(2)+e_(2)^(2))sin(omegat+phi)`
Where, `cosphi = (e_(1))/(sqrt(e_(1)^(2)+e_(2)^(2)))` and `sinphi = (e_(2))/(sqrt(e_(1)^(2)+e_(2)^(2)))`
i.e., `e_(0) = sqrt(e_(1)^(2)+e_(2)^(2))`
or `e_(rms) = sqrt(e_(1)^(2)+e_(2)^(2))/(sqrt(2))`