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Found in: Page 862

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# The $$4.00{\rm{ }}A$$ current through a $$7.50{\rm{ }}mH$$ inductor is switched off in $$8.33{\rm{ }}ms$$. What is the emf induced opposing this?

The $$4.00{\rm{ }}A$$ current through a $$7.50{\rm{ }}mH$$ inductor is switched off in $$8.33{\rm{ }}ms$$. The emf opposing this is, $$\varepsilon = - 3.6\;V$$.

See the step by step solution

## Step 1: Concept Introduction

A current produced by the creation of voltage (electromotive force) in the presence of a shifting magnetic field is known as electromagnetic induction.

This happens when a conductor is placed in a magnetic field that is moving (using an AC power source) or when a conductor is continuously moving in a magnetic field that is stationary.

## Step 2: Information Provided

• Inductance of the inductor:

$$\begin{array}{c}M = 7.50{\rm{ }}mH = \frac{{7.50}}{{1000}}\\ = 0.0075{\rm{ }}H\end{array}$$.

• Current through an inductor: $$4.00{\rm{ }}A$$.
• Time in which current is switched off:

$$\begin{array}{c}t = 8.33{\rm{ }}ms = \frac{{8.33}}{{1000}}\\ = 0.00833{\rm{ }}s\end{array}$$.

## Step 3: Calculation for the voltage

The formula for the induced electromotive force is –

$$\varepsilon = - M\frac{{\Delta I}}{{\Delta t}}$$

After substituting the values, the calculation is –

$$\begin{array}{c}\varepsilon = - 0.0075 \cdot \frac{4}{{0.00833}}\\ = - 3.6\;V\end{array}$$

Therefore, the value for emf is obtained as $$\varepsilon = - 3.6\;V$$.