7.0 Inductor and Inductance:

7.1 Inductors connected in series:
7.2 Inductors connected in parallel:
7.3 Mutually coupled inductors in parallel:

Whenever is current in changed in a conducting coil emf is induced in it. The property of the coil of inducing emf due to the changing of magnetic flux linked with it is known as inductance of the coil. Due to this property all electrical coil can be referred as inductor. Inductors are formed with wire tightly wrapped around a solid central core which can be either a straight cylindrical rod or a continuous loop or ring to concentrate their magnetic flux.

When a current is established in a closed conducting loop, because of current there is a magnetic field. Magnetic field has its magnetic flux through the area of loop. Whenever current change, magnetic flux start to change. We know if flux change through a closed conducting loop then emf is induced in this loop. This is process is called self induction.

Magnetic field in a coil depends on current flowing into coil. Assume that area of coil is constant. So magnetic flux through this closed conducting loop is proportional to current. So we can say,

${\Phi _B} \propto i$

${\Phi _B} = Li$

This proportionality constant is called self inductance of the loop. Self inductance is a constant depends on the geometry of loop. Induced emf in coil when current changes,

$\varepsilon = - \frac{{d{\Phi _B}}}{{dt}}$

$ = - L\frac{{di}}{{dt}}$

The $SI$ unit of self inductance $L$ is Weber amphere-1 or volt second amphere-1. It is a given special name Henry and is abbreviated as $H$.

Consider two closed conducting loop is placed near to each other. If a current is flowing in one loop so there is a magnetic field because of this current. If this magnetic field is passing through second loop so this magnetic field has flux enclosed by the area of second loop. As magnetic field is proportional to current producing it, so

${\Phi _B} \propto i$

${\Phi _B} = Mi$

This proportionality constant is called mutual inductance. This constant depends on the geometrical shape of both loops.

Let us consider two coils, second coils have $N$ loops. If current in first coil is $i$ and produced magnetic field is $B$. Consider ${\Phi _B}$ is magnetic flux through one loop of second coil so total magnetic flux is $N{\Phi _B}$. By this we can say induced emf is,

$\varepsilon = - N\frac{{d{\Phi _B}}}{{dt}}$

$ = - MN\frac{{di}}{{dt}}$

The $SI$ unit of self induction $H$ is Weber amphere-1 or volt second amphere-1. It is a given special name Henry and is abbreviated as $H$.