A d.c. voltage with appreciable ripple expressed as `V = V_(1) + V_(2) cos omega t ` is applied is a resistor The amount of heat generated per second is given by

Options

A. `(V_(1)^(2) + V_(2)^(2))/(2R)`
B. `(2V_(1)^(2) + V_(2)^(2))/(2R)`
C. `(V_(1)^(2) +2 V_(2)^(2))/(2R)`
D. none of the above

Answer

b

Explanation

Heat generated per sec
`H = (V^(2))/(R ) = ((V_(1) + V_(2) cos omega t)^(2))/(R)`
`=(V_(1)^(2)+V_(2)^(2)cos^(2) omegat+2V_(1)V_(2)cos omegat)/(R)`
Average value of `cos^(2) omega t ` over a cycle `= (1)/(2)`
Average value of `cos omega t ` over a cycle `= 0`
`:.` Heat generated per second,
`H = (V_(1)^(2) + V_(2)^(2)xx(1)/(2) +2V_(1)V_(2) xx 0)/(R ) = (2V_(1)^(2) + V_(2)^(2))/(2R)`