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

Answer 1

The correct option is 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, $P_{i}nstantaneous=EI=E_{0}sin\omega t\times i_{0}sin(\omega t-\frac{\pi }{2})=E_0{i}_{0}sin\omega t(sin\omega tcos\frac{\pi }{2}-cos\omega tsin\frac{\pi }{2})=E_0{i}_{0}sin\omega tcos\omega t=\frac{1}{2}{E}_0{i}_{0}sin2\omega t(sin2sin\omega t=2sin\omega tcos\omega t)$
Hence, angular frequency of instantaneous power is $2\omega$