Question

A12 Hinductor carries a current of2.0 A. At what rate must the current be changed to produce a60 Vemf in the inductor?

Short answer

$\frac{di}{dt}=-\text{5.0}\text{A/s}$

Step-by-step solution

Given

1. Inductance of inductor, $L=12.0\text{H}$
2. Current through inductor,$i=2.0\text{A}$
3. Emf induced, $\epsilon =60\text{V}$

Understanding the concept

We can use Faraday’s law of electromagnetic induction and the definition of inductance to find the rate of change of current through the inductor.

Formula:

$\epsilon =-\frac{d{\varphi }_B}{dt}$

${\varphi }_B=Li$

Calculate at what rate must the current be changed to produce a emf in the inductor

We have

$\epsilon =-\frac{d{\varphi }_B}{dt}=-\frac{d}{dt}\left(Li\right)$

As the inductance is fixed for a given inductor, then

$\epsilon =-\frac{d{\varphi }_B}{dt}=-L\frac{di}{dt}$

So using the above equation we get

$\frac{di}{dt}=-\frac{\epsilon }{L}=\frac{60}{12.0}=\text{- 5.0}\text{A/s}$