Question

The coefficient of mutual induction between two coils is 4 H. If the current in the primary reduces from 5 A to zero in ${10^{ - 3}}$ second then the induced emf in the secondary coil will be
(a). ${10^4}V$
(b). $25 \times {10^3}V$
(c). $2 \times {10^4}V$
(d). $15 \times {10^3}V$

Answer 1

- Hint: In this question the concept of mutual inductance is used that is if two coils of wire are brought into close proximity with each other so the magnetic field from one links with the other, a voltage will be generated in the second coil as a result. This is called mutual inductance when voltage impressed upon one coil induces a voltage in another.
Formula used : Electro motive force i.e. $emf = - M\dfrac{{dI}}{{dt}}$.

Complete step-by-step solution -

According to the question the coefficient of mutual induction between two coils is 4 H and it is there that the if the current in the primary reduces from 5 A to zero in ${10^{ - 3}}$ second so we have to find the induced emf in the secondary coil.
Hence, $emf = - M\dfrac{{dI}}{{dt}}$
$= - 4 \times \dfrac{{0 - 5}}{{{{10}^{ - 3}}}} = 2 \times {10^4}V$

Note: There are two types of induction i.e. self and mutual where as self induction is when the current flows in coil changes, an induced current is produced in the same coil , where as mutual induction is when 2coils are placed near each other and current is changing in one coil, an induced current is produced in another coil. Use these concepts while involving into such types of questions.