Question

An alternating emf of angular frequency $\omega$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency :

• A. $\frac{\omega }{4}$
• B. $\frac{\omega }{2}$
• C. $\omega$
• D. $2\omega$

Answer 1

Answer: (D)

$2\omega$

The instantaneous values of emf and current in inductive circuit are given by

$[E=E_0\sin \omega t]$ and $[i=i_0\sin (\omega t-\frac{\pi }{2})]$ respectively.

So, $[P_{inst}=Ei=E_0\sin \omega t\times i_0\sin (\omega t-\frac{\pi }{2})]$

$[=E_0{i}_0\sin \omega t(\sin \omega t\cos \frac{\pi }{2}-\cos \omega t\sin \frac{\pi }{2})]$

$[=E_0{i}_0\sin \omega t\cos \omega t]$

$[=\frac{1}{2}{E}_0{i}_0\sin 2\omega t]$

$\left[\right(\sin 2\omega t=2\sin \omega t\cos \omega t\left)\right]$

Hence, angular frequency of instantaneous power is $\left[2\omega \right].$