**Inductor in Series and Parallel**

**Inductor in Series: **Inductor in series are inductors that are placed back – to – back. Below is a circuit where 3 inductors are placed in series.

You can see the inductors are in series because they are back – to – back against each other. The best way to think of a series circuit is that if current flows through the circuit, the current can only take one path. You can see in the above circuit that if current flowed through it, it could only take one path.

**Formula for Adding Inductors in Series: **The formula to calculate the total series inductance of a circuit is L_{T} = L₁ + L₂ + L₃ + …

So to calculate the total inductance of the circuit above, the total inductance, L_{T} would be L_{T} = 10H + 20H + 30H – 60H.

So using the above formula, the total inductance is 60H.

When inductors are in series, as the formula shows, they simply add together. Thus, the total inductance of a series circuit will always be greater than any of the individual inductor values.

**Inductor in Parallel: **Inductor in parallel are inductors that are connected side – by – side in different branches of a circuit. Below is a circuit where 3 inductors are in parallel.

You can see that the inductors are in parallel because they are all on their own separate branches in the circuit. The best way to think about parallel circuits is by thinking of the path that current can take. When current is travelling through a parallel circuit, the current can take various paths through the circuits, such as to go through any of the branches containing the inductors. In series, this is not the case. Current can only take one path.

**Formula for Adding Inductors in Parallel: **The formula to calculate the total parallel inductance is \({{L}_{T}}\,=\,\frac{1}{\frac{1}{{{L}_{1}}}+\frac{1}{{{L}_{2}}}+\frac{1}{{{L}_{3}}}+…….+etc}\).

So to calculate the total inductance of the circuit above, the total inductance, L_{T} would be \({{L}_{T}}\,=\,\frac{1}{\frac{1}{10H}+\frac{1}{20H}+\frac{1}{30H}}\) = 5.45H.

So using the above formula, the total inductance is 5.45Ω.

When inductors are in parallel, the total inductance value is always less than the smallest inductor of the circuit. In other words, when inductors are in parallel, the total inductance shrinks. It’s always less than any of the values of the inductors.