Question

An alternating e.m.f. of angular frequency `omega` is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency
A. `(omega)/4`
B. `(omega)/2`
C. `omega`
D. `2 omega`

Answer 1

Correct Answer - D
The instataneous values of e.m.f and current in inductive circuit are given by `E=E_(0)sin omegat` and `i=i_(0)sin(omegat-(pi)/2)` respectively.
So, `P_("inst")=Ei=E_(0)sin omegatxxi_(0)sin(omegat-(pi)/2)`
`=E_(0)i_(0)sin omega t(sin omegat cos ((pi)/2)-cos omegat sin ((pi)/2))`
`=E_(0)i_(0)sin omegat cos omegat`
`=1/2E_(0)i_(0)sin 2 omegat(sin 2omegat=2sin omegatcos omegat)`
Hence, angular frequency of instantaneous power is `2omega`.