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When an a.c. source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero. |
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Answer» SOLUTION :Let an ALTERNATING voltage `V = V_(m) sin omega t`is applied across an ideal capacitor, then current setup in the CIRCUIT is given by `I = I_(m) sin (omega t + pi/2)` `therefore` Average power for one complete cycle of circuit will be `P_(av) = 1/T int _(0)^(T) V I dt = 1/T int_(0)^(T) V_(m) sin omega. I_(m) sin(omega t + pi/2). dt = (V_(m)I_(m))/2 int_(0)^(T) sin OMEGAT.cos omegat dt` `=(V_(m)I_(m))/(4 o mega T) [-cos 4PI + cos 0] = (V_(m)I_(m))/(4 omega T) [-1+1]=0` |
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