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 :
- 6 mH
- 12 mH
- 3 mH
- 9 mH
The Correct Option is C
Solution and Explanation
The induced emf (E) in a coil is related to the rate of change of current by the formula:
Formula for induced emf:
\( E = -L \frac{\Delta I}{\Delta t} \)
where:
- E = 1.5 V is the induced emf
- L is the self-inductance
- \(\Delta I\) = 8 - 6 = 2 A is the change in current
- \(\Delta t\) = 4 ms = \( 4 \times 10^{-3} \) s is the time interval
Rearranging the formula to solve for L:
Rearranged formula:
\( L = \frac{E \Delta t}{\Delta I} \)
Substituting the given values:
\( L = \frac{(1.5)(4 \times 10^{-3})}{2} = 3 \times 10^{-3} \, \text{H} = 3 \, \text{mH} \)
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