Question

An alternating e.m.f. of angular frequency 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, $P_{inst}=E_i=E_{0}sin\omega t\times i_{0}sin(\omega t-\frac{\pi }{2})$
$=E_0{i}_{0}sin\omega t(sin\omega tcos\frac{\pi }{2}-cos\omega tsin\frac{\pi }{2})$
$=E_0{i}_{0}sin\omega tcos\omega t$
$=\frac{1}{2}{E}_0{i}_{0}sin2\omega t$ $(sin2\omega t=2sin\omega tcos\omega t)$
Hence, angular frequency of instantaneous power is 2$\omega$.