Inductors are said to be connected together in “Parallel” when both of their terminals are respectively connected to each terminal of the other inductor or inductors. The voltage drop across all of the inductors in parallel will be the same. Then, Inductors in Parallel have aCommon Voltage across them and in our example below the voltage across the inductors is given as:
VL1 = VL2 = VL3 = VAB …etc
In the following circuit the inductors L1, L2 and L3 are all connected together in parallel between the two points A and B.
Inductors in Parallel Circuit
In the previous series inductors tutorial, we saw that the total inductance, LT of the circuit was equal to the sum of all the individual inductors added together. For inductors in parallel the equivalent circuit inductance LT is calculated differently.
The sum of the individual currents flowing through each inductor can be found using Kirchoff’s Current Law (KCL) where, IT = I1 + I2 + I3 and we know from the previous tutorials on inductance that the self-induced emf across an inductor is given as: V = L di/dt
Then by taking the values of the individual currents flowing through each inductor in our circuit above, and substituting the current i for i1 + i2 + i3 the voltage across the parallel combination is given as:
By substituting di/dt in the above equation with v/L gives:
We can reduce it to give a final expression for calculating the total inductance of a circuit when connecting inductors in parallel
