Inductors are connected in series and parallel, when an inductor is connected in a circuit, that connection can be either series or parallel. What will happen to the total current, voltage, and Inductance values if they are connected in series even when they are connected in parallel?
Inductor Connection in Series
When inductors are chained together in a straight line or they are connected end to end, inductors are said to be in a series connection. We know that when resistors are connected in series, their effective resistance increases.
Similarly, when inductors are connected in series, their effective inductance increases. Inductors in series are similar to capacitors in parallel. To get total inductance is very simple. All you have to do is add each inductance. That is, when the inductors are connected in series, the total inductance is the sum of all the inductances.
There are three inductors here and are connected in series. In this case, the current flowing through each inductor is the same while the voltage across each inductor is different. This voltage depends on the inductance value.
According to Kirchhoff’s Voltage Law, the voltage around a loop is equal to the sum of each voltage drop in the same loop and equal to zero for any closed network.
Using Kirchhoff’s voltage law, the total voltage drop is the sum of the voltage drops across each inductor. he is:
We know that the voltage across an inductor is given by the equation:
So here we can write,
But
Therefore,
Inductor Connection in Parallel
If two terminals of one inductor are connected to two terminals of another inductor, the inductors are said to be parallel. We know that when resistors are connected in parallel, their effective resistance decreases. Similarly, when inductors are connected in parallel, their effective inductance decreases. Inductors in parallel are somewhat similar to capacitors in series.
Here, the current flowing through each inductor will be different. This current depends on the inductance value. However, the voltage across each conductor will be the same.
According to Kirchhoff’s Current Law, The total current entering a junction or node is equal to the charge leaving the node as no charge is lost.
Using Kirchhoff’s current law the total current is the sum of the current through each branch. that is:
We know that the voltage across an inductor is given by the equation,
we can write,
We can further write it as
That is
Since the voltages are equal, we can simplify the equation,
