SATHEE: Electro Magnetic Induction And Alternating Currents Question 135

Electro Magnetic Induction And Alternating Currents Question 135

Question: An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency [Roorkee 1999]

Options:

A) $\frac{ω}{4}$

B) $\frac{ω}{2}$

C) $ω$

D) $2 ω$

Show Answer

Answer:

Correct Answer: D

Solution:

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

$E = E_{0} \sin ω t$ and $i = i_{0} \sin (ω t - \frac{π}{2})$ respectively.

So, $P_{i n s t} = E i = E_{0} \sin ω t \times i_{0} \sin (ω t - \frac{π}{2})$

$= E_{0} i_{0} \sin ω t (\sin ω t \cos \frac{π}{2} - \cos ω t \sin \frac{π}{2})$

$= E_{0} i_{0} \sin ω t \cos ω t$ $= \frac{1}{2} E_{0} i_{0} \sin 2 ω t$ $(\sin 2 ω t = 2 \sin ω t \cos ω t)$

Hence, angular frequency of instantaneous power is $2 ω$ .

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Electro Magnetic Induction And Alternating Currents Question 135

Question: An alternating e.m.f. of angular frequency ω is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency [Roorkee 1999]

Options:

Answer:

Solution:

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Question: An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency [Roorkee 1999]