Question

A 12V battery connected to a coil of resistance 6Ω through a switch, drives a constant current in the circuit. The switch is opened in 1ms. The emf induced across the coil is 20V. The inductance of the coil is:

• A. 5mH
• B. 8mH
• C. 10mH
• D. 12mH

Answer 1

The Correct Option is C

Understanding the Problem

We are given the induced emf in a coil and the rate of change of current, and we need to find the inductance of the coil.

Solution

1. Formula for Induced EMF:

The induced emf in a coil is given by:

\( e = -L \frac{di}{dt} \)

where:

• \( e \) is the emf induced across the coil
• \( L \) is the inductance
• \( \frac{di}{dt} \) is the rate of change of current

2. Given Values:

• \( e = 20 \, \text{V} \)
• \( R = 6 \, \Omega \) (not needed for this calculation)
• \( i = 2 \, \text{A} \) (initial current)
• \( \frac{di}{dt} = \frac{0 - 2}{10^{-3}} = -2 \times 10^3 \, \text{A/s} \)

3. Substitute Values into the Formula:

\( 20 = -L \times (-2 \times 10^3) \)

4. Solve for Inductance (L):

\( L = \frac{20}{2 \times 10^3} \)

\( L = 10 \times 10^{-3} \, \text{H} \)

\( L = 10 \, \text{mH} \)

Final Answer

The inductance of the coil is \( 10 \, \text{mH} \).