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. $2\omega$
• D. $4\omega$

Answer 1

Answer: (C)

$V=V_0\sin \omega t$
If it is applied across an inductor, then $I$ lag by $\frac{\pi }{2}.$ Thus
$I=I_0\sin \left(\omega t-\frac{\pi }{2}\right)$
$P=VI=V_0{I}_0\sin \omega t\sin \left(\omega t-\frac{\pi }{2}\right)$
$=-\left(\frac{V_0{I}_0}{2}\right)2\sin \omega t\cos \omega t$
$P=-\left(\frac{V_0{I}_0}{2}\right)\sin (2\omega t)$
$P=\frac{V_0{I}_0}{2}\sin (2\omega t+\pi )$
$\Rightarrow P$ has an angular frequency of '$2{\omega }^{\prime }$'.