Question

A primary coil and a secondary coil are placed close to each other. A current, which changes at the rate of \[25amp\] in a\[milli\sec \], is present in the primary coil. If the mutual inductance is \[92\times {{10}^{-6}}H\], then the value of induced emf in the secondary coil is:
 \[\begin{align}
  & A)4.6V \\
 & B)2.3V \\
 & C)0.368mV \\
 & D)0.23mV \\
\end{align}\]

Answer 1

Hint: If two coils are placed closer to each other and one coil has a change in current passed through, an emf will be generated. This is due to the interaction of one coils magnetic field with another. This emf is given as the product of mutual inductance between the two coils and the rate of change of current passed through the primary coil.
Formula Used: \[e=M\dfrac{\delta I}{\delta t}\]

Complete solution: Firstly we must be aware of mutual inductance. When we place two coils close, the magnetic field of one coil interacts with the other coil as it induces a voltage in the adjacent coil.
The induced emf\[e\]is proportional to the rate of change of current through primary coil and this proportionality constant is called Mutual inductance (\[M\]).
So, mutually induced emf \[e\] is expressed as,
\[e=M\dfrac{\delta I}{\delta t}\]
Here, the mutual inductance \[M\] is given as \[92\times {{10}^{-6}}H\] and rate of change of current\[\dfrac{\delta I}{\delta t}\] is given as \[25A/milli\sec \].
Now, induced emf is,
\[\begin{align}
  & e=M\dfrac{\delta I}{\delta t} \\
 & e=92\times {{10}^{-6}}\times \dfrac{25}{{{10}^{-3}}} \\
 & e=2.3V \\
\end{align}\]
So, induced emf \[e\] is found to be \[2.3V\]. The correct answer is option B.

Note: This induced emf due to mutual induction can be found in another way. The expression is given as \[e={{N}_{{}}}\dfrac{\delta {{\phi }_{{}}}}{\delta t}\] where \[N\] is no of turns of the secondary coil and \[\phi \]is the magnetic flux change. While doing the problem we must be aware of the coil which is having the flux as it will be having the current change.