Question

A coil has a self-inductance of \(2H\); find the induced EMF if the current changes from \(5A\) to \(2A\) in \(0.1\) seconds.

• A. \(30V\)
• B. \(40V\)
• C. \(50V\)
• D. \(60V\)

Hint:

Induced EMF in inductors follows \[ e = L\frac{di}{dt} \] A faster change in current produces a larger induced EMF.

Answer 1

The Correct Option is D

Concept: The induced EMF in a coil is given by the relation: \[ e = \left|L\frac{di}{dt}\right| \] where \(L\) is the self-inductance and \(\frac{di}{dt}\) is the rate of change of current.

Step 1: Calculate the change in current. \[ di = 5 - 2 = 3A \]

Step 2: Write the time interval. \[ dt = 0.1\,s \]

Step 3: Substitute into the EMF formula. \[ e = L\frac{di}{dt} \] \[ e = 2 \times \frac{3}{0.1} \] \[ e = 2 \times 30 \] \[ e = 60V \] Thus, the induced EMF is: \[ \boxed{60V} \]