The source transformation technique is required to simplify an electric circuit for analysis.
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,
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 an equivalent current source and a current source can also be converted into an equivalent voltage source.
If you’d prefer a video explanation on current to voltage source conversion, take a look at the video below:
Voltage Source to Current Source Conversion
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
Hence, voltage appearing, across the source, when terminals are open, is V.