Physics > Electromagnetic Induction > 7.0 Inductor and Inductance:
Electromagnetic Induction
1.0 Introduction
2.0 Magnetic Flux
3.0 Experiments by Faraday and Henry
4.0 Len’z Law:
5.0 Induced Electric Field
6.0 Eddy Current:
7.0 Inductor and Inductance:
7.1 Inductors connected in series:
7.2 Inductors connected in parallel:
7.3 Mutually coupled inductors in parallel:
8.0 Growth and Decay of current in an LR circuit:
7.2 Inductors connected in parallel:
7.2 Inductors connected in parallel:
7.3 Mutually coupled inductors in parallel:
In previous section total inductance of a circuit is the sum of individual inductance of inductors. But if inductors are connected in parallel then there is a different way to calculate total inductance.
In parallel case, by Kirchhoff’s law we can found total current, it is the sum of the individual current passing through inductors.
By Kirchhoff’s law,
$$I = {I_1} + {I_2} + {I_3}$$
And we know that the induced emf in an inductor is Ldi/dt
$${V_{AB}} = L\frac{{di}}{{dt}}$$
Substituting, $\frac{{di}}{{dt}} = \frac{V}{L}$
$${V_{AB}} = {L_T}\left( {\frac{V}{{{L_1}}} + \frac{V}{{{L_2}}} + \frac{V}{{{L_3}}}} \right)$$
or, $${\frac{1}{L}_T} = \left( {\frac{1}{{{L_1}}} + \frac{1}{{{L_2}}} + \frac{1}{{{L_3}}}} \right)$$
