Question

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?

Short answer

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, \(\varepsilon = - 3.6\;V\).

Step-by-step solution

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.

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:

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

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 \(\varepsilon = - 3.6\;V\).