Question 22: Electromagnetic Induction

Question

One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from $$3 \mathrm{~A}$$ to $$1 \mathrm{~A}$$ in 100 milliseconds. the mutual inductance of the two coil is:

Accepted Answer

To find the mutual inductance (M) between the two coils given the induced emf (voltage change) in the secondary coil when the current in the primary coil changes, we can use the formula for induced emf due to mutual inductance:
$$ emf = -M \frac{\Delta I}{\Delta t} $$
where:
$ emf $ is the induced electromotive force (in volts, V)
$ M $ is the mutual inductance between the coils (in henries, H)
$ \Delta I $ is the change in current (in amperes, A)
$ \Delta t $ is the time over which the current changes (in seconds, s)
Given values are:
$ emf = 1 \, \mathrm{V} $
$ \Delta I = I_{final} - I_{initial} = 1 \, \mathrm{A} - 3 \, \mathrm{A} = -2 \, \mathrm{A} $
$ \Delta t = 100 \, \mathrm{milliseconds} = 100 	imes 10^{-3} \, \mathrm{s} = 0.1 \, \mathrm{s} $
Plugging these values into the formula, we solve for $ M $:
$$ 1 = -M \frac{-2}{0.1} $$
$$ M = \frac{1}{2} 	imes 0.1 $$
$$ M = 0.05 \, \mathrm{H} $$
Therefore, the mutual inductance of the two coils is 0.05 H, which corresponds to Option D.

Answer

0.5 H

Answer

0.25 H

Answer

0.005 H

Answer

0.05 H

Electromagnetic Induction

One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from $3 \mathrm{~A} to 1 \mathrm{~A}$ in 100 milliseconds. the mutual inductance of the two coil is:

Choose the correct answer: