## Tuesday, September 13, 2016

### Finding Self Induction and Inductors in Series and Parallel

Finding self-inductance of a coil

Self inductance is the property of a coil by virtue of which it opposes the change in the magnetic flux causing it. A galvanometer connected to the circuit of the coil shown the deflection change only when there is a change in the switch mode that is during on and off mode. It indicates that the induced EMF is generated only during that time.

The magnitude of the induced current developed in a coil is directly proportional to the magnetic flux generated in that coil. We can eliminate the proportionality using a constant called self inductance coefficient.

We can find the magnetic flux in a coil using the concept that it is the dot product of magnetic field induction and area of cross section.

Further using the concept that the flux is the product of self induction constant and induced current, we can find the self induction constant as shown in the diagram below.

Similarly we can also find the mutual induction coefficient as shown in the diagram below.

Inductance coils connected in series and parallel

We can measure the effective induction coefficient when the coils are connected in series and parallel. When the coils are in series, the current in each coil is same to the current passing in the circuit. We also know that the emf of the circuit is the sum of total emfs in the circuit.

Using that concept we can find the effective coefficient when the coils are connected in series as the sum of individual coefficients. When the coils are connected in parallel, the current of the system is shared across the coils and emf of the circuit is similar to the emf of the coil.

Thus we can measure the effective coefficient as shown in the diagram below.

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