Question

Define coefficient of mutual induction. If in the primary coil of a transformer, the current decreases from 0.8A to 0.2A in 4 milliseconds, calculate the induced EMF in the secondary coil. Mutual inductance is 1.76H.

Answer 1

Hint – To find the induced EMF/voltage in the other coil we use the concept of faraday’s law of electromagnetic induction and use the formula for Mutual Inductance. We substitute the given data in it to derive the induced voltage.
Formula used: ${\text{M = }}\dfrac{{{\varepsilon _{{\text{emf}}}}}}{{\left( {\dfrac{{{\text{dI}}}}{{{\text{dt}}}}} \right)}}$, where M is the mutual inductance, ε is the EMF induced into the other coil and $\dfrac{{{\text{dI}}}}{{{\text{dt}}}}$ is the rate of change of current in the given coil.

Complete step-by-step solution -
Mutual inductance is a measure of induction between two different circuits. It is the ratio of the electromotive force in a circuit to the corresponding change of current in neighboring circuit and it is mathematically defined as ratio of induced EMF due to change in current of the other loop/circuit divided by the rate of change of the current in the other circuit.
It is usually measured in henries (H).
Let us consider two circuits as follows:

In which current passes in the second circuit such that the rate of change of current is non-zero, i.e. $\dfrac{{{\text{dI}}}}{{{\text{dt}}}} \ne 0$. Due to this change of current, the lines of flux passing through the circuit will also change. Now according to Faraday's law of electromagnetic Induction this will give rise to an induced EMF in the first circuit.
Mutual inductance is given by ${\text{M = }}\dfrac{{{\varepsilon _{{\text{emf}}}}}}{{\left( {\dfrac{{{\text{dI}}}}{{{\text{dt}}}}} \right)}}$.
Given Data,
Current decreases from 0.8A to 0.2A in 4 milliseconds and M = 1.76H.
$ \Rightarrow {\text{M}}\left( {\dfrac{{{\text{dI}}}}{{{\text{dt}}}}} \right){\text{ = }}{\varepsilon _{{\text{emf}}}}$ ----------- (1 second = 1000 milliseconds)
Induced EMF = $1.76{\text{ }} \times {\text{ }}\dfrac{{0.8{\text{ - 0}}{\text{.2}}}}{{4{\text{ }} \times {\text{ 1}}{{\text{0}}^{ - 3}}}}$= 264 V.
Hence the induced EMF in the secondary coil is 264 Volts.

Note – In order to answer this type of questions the key is to know a few concepts such as faraday’s laws of electromagnetism, terms like EMF and mutual inductance.
Faraday’s laws of electromagnetic induction are - Whenever a conductor is placed in a varying magnetic field, EMF induces and this EMF is called an induced EMF and if the conductor is a closed circuit then the induced current flows through it. The magnitude of the induced EMF is equal to the rate of change of flux linkages. Electromotive force or EMF is a measurement of the energy that causes current to flow through a circuit. It is measured in volts (V).