Question

When current in a coil changes at a steady rate from 8 A to 6 A in 4 ms, an emf of 1.5 V is induced in it. The value of self-inductance of the coil is :

• A. 6 mH
• B. 12 mH
• C. 3 mH
• D. 9 mH

Answer 1

The Correct Option is C

The induced electromotive force (emf), denoted by E, in a coil is proportional to the rate at which the current changes, as expressed by the following formula:

Formula for induced emf:
\( E = -L \frac{\Delta I}{\Delta t} \)

In this equation:

• E represents the induced emf, given as 1.5 V.
• L denotes the self-inductance.
• \(\Delta I\) is the change in current, calculated as 8 A − 6 A = 2 A.
• \(\Delta t\) is the time interval over which the current change occurs, specified as 4 ms, which is equivalent to \( 4 \times 10^{-3} \) s.

To determine the self-inductance (L), the formula can be rearranged:

Rearranged formula:
\( L = \frac{E \Delta t}{\Delta I} \)

Substituting the provided values into the rearranged formula yields:

\( L = \frac{(1.5 \, \text{V})(4 \times 10^{-3} \, \text{s})}{2 \, \text{A}} = 3 \times 10^{-3} \, \text{H} \)

Therefore, the self-inductance L is 3 mH.