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

Options

A. `2 omega`
B. `omega`
C. `(omega)/4`
D. `(omega)/2`

Answer

A

Explanation

For a pure inductance, the current lags behind the voltage by `(pi)/2`.
`:.` For the circuit, `E=E_(0)I_(0) sin omega t sin(omega t = (pi)/2)`
`= E_(0)I_(0) sin omega t (-cos omega t)`
`=E_(0)I_(0) sin omega t cos omega t`
`1/2 E_(0)I_(0)(sin 2 omegat)`
Thus the angular frequency of the instantaneous power is `2 omega`.