In a series LCR circuit , and alternating emf (v) and current (i) are given by the equation `v=v_(0) sin omegat, i=i_(0)sin (omegat+(pi)/(3))`. The average power dissipated in the circuit over a cycle of AC is

Options

A. `(v_(0)i_(0))/(2)`
B. `(V_(0)i_(0))/(4)`
C. `(sqrt3)/(2)v_(0)i_(0)`
D. Zero

Answer

b

Explanation

In a series LCR circuit,
`V= V_(0)sin omegat` and `i= i_(0)sin (omegat+ (pi)/(3))`
Average power dissipated over a cycle ,
`P= V_(rms)i_(rms)cosphi`
`= (V_(0))/(sqrt2)xx(i_(0))/(sqrt2)xxcos(pi)/(3)= (v_(0)i_(0))/(4)`