Question

An alternating electromagnetic force 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 applied voltage,

$V=V_{0}sin\omega t$

The current flowing in the circuit,

$I=I_{0}sin(\omega t-\frac{\pi }{2})$

The instantaneous power developed in the circuit

$P=V.I$

$P=V_{0}sin\omega t.I_{0}sin(\omega t-\frac{\pi }{2})$

$P=I_0{V}_0.sin\omega t.(sin\omega t.cos\frac{\pi }{2}+cos\omega t.sin\frac{\pi }{2})$

$P=I_0{V}_0.sin\omega t(sin\omega t\times 0+cos\omega t\times 1)$

$P=I_0{V}_{0}sin\omega t.cos\omega t$

$P=\frac{I_0{V}_0}{2}.2sin\omega t.cos\omega t$

$P=\frac{I_0{V}_0}{2}.sin2\omega t$

The instantaneous power developed in the circuit has an angular frequency $2\omega .$

The correct option is D.