# Electrical Source Transformation

**Electrical source transformation** is a method of replacing voltage source in a circuit by its equivalent current source and current source by its equivalent voltage source.

The

**source transformation** technique is required to simplify an electric circuit for analysis.

Let us take a simple

voltage source along with a

resistance connected in series with it. This series resistance normally represents the internal resistance of a practical

voltage source.

Now, let us short circuit the output terminals of the

voltage source circuit as shown below,

Now, applying

Kirchhoff Voltage Law in the circuit above we get,

Where, I is the current delivers by the voltage source when it is short circuited.

Now, let us take a current source of same current I which produces same open circuit voltage at its open terminals as shown below,
Now, applying Kirchhoff Current Law at node 1, of the above circuit, we get,
From equation (i) and (ii) we get,
The open circuit voltage of both the sources is V and short circuit current of both sources is I. The same resistance connected in series in voltage source is connected in parallel in its equivalent current source.

So, these voltage source and current source are equivalent to each other.
A current source is dual form of a voltage source and a voltage source is dual form of a current source. A voltage source can be converted into equivalent current source and a current source can also be converted into equivalent voltage source.

### Voltage Source to Current Source Conversion

Assume a

voltage source with terminal voltage V and the internal resistance r. This resistance is in series. The current supplied by the source is

when the source of the terminals are shorted.
This current is supplied by the equivalent

current source and same resistance r will be connected across the source.

Voltage source to

current source conversion is shown in the following figure.

### Current Source to Voltage Source Conversion

Similarly assume a

current source with value I and internal resistance r. Now according to the

Ohm’s law the voltage across the source can be calculated as

Hence, voltage appearing, across the source, when terminals are open, is V.