JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II NETWORK THEORY Previous Question Paper (March - 2021 - R16)

Faraday's laws of electromagnetic induction describe the relationship between magnetic fields and electric circuits. The first law states that an electromotive force (EMF) is induced in a conductor whenever it is placed in a varying magnetic field or when the conductor moves through a magnetic field. For example, moving a permanent magnet toward a stationary coil causes a deflection in a connected galvanometer, indicating current flow.

The second law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit. Mathematically, this is expressed as:

Here, e is the induced EMF, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux. The negative sign represents Lenz's Law, indicating that the induced EMF opposes the change in flux that produced it. An example is a transformer, where a time-varying current in the primary winding induces an EMF in the secondary winding due to the changing magnetic flux.

The coefficient of coupling (k) is a measure of the magnetic coupling between two coils. It represents the fraction of the total magnetic flux produced by one coil that links with the other coil. It is a dimensionless quantity ranging from 0 (no coupling) to 1 (perfect coupling).

To derive the expression, consider two coils with self-inductances L1 and L2. Let Φ1 be the flux produced by coil 1, where a portion k1Φ1 links with coil 2. Similarly, let Φ2 be the flux produced by coil 2, where k2Φ2 links with coil 1. The mutual inductance M is given by:

Since L1 = N1 * (Φ1 / I1) and L2 = N2 * (Φ2 / I2), we can write:

Where k = sqrt(k1 * k2). Thus, the coefficient of coupling is defined as:

This expression shows that the mutual inductance between two coils is limited by the product of their individual self-inductances and the degree of magnetic linkage between them.