# Source Transformation in Electrical Circuits

Source transformation is a method used for circuit simplification by replacing the voltage source with its equivalent current source or replacing the current source with its equivalent voltage source.

For ideal electrical sources, losses will be zero. In the case of practical sources, losses will be there because of its internal resistance or impedance. In the discussion below, we have considered the practical case.

The practical voltage source consists of a voltage source in series with its internal resistance. Similarly, the practical current source consists of the current source in parallel with its internal resistance.

Now, let’s learn how the transformation is done from one source to another.

## Voltage source to current source transformation

Let us consider a circuit with practical voltage source V_{s} having internal resistance R_{s}, connected to the load having resistance R_{L}.

Now, in this circuit, let us understand, how the voltage source in series with the internal resistance is replaced with its equivalent current source.

In the circuit, the current delivered to the load is given by,

Since it is a series circuit, I = I_{L}

Now, if the voltage source is to be replaced by the current source I, then the internal resistance should be connected across the current source.

By current divider rule, the load current I_{L} will be

From equations (1) and (2),

Thus is it observed that in transforming the voltage source, the obtained current source(3) is connected with internal resistance R_{s} in parallel with the source.

## Current source to voltage source transformation

Consider a circuit with the practical current source I in parallel with its internal resistance R_{s}, connected to the load having resistance R_{L}.

As discussed above and from equation (3), a current source in parallel with the internal resistance is transformed into the voltage source V_{s} by placing the internal resistance in series with the source, where *V _{s} = IR_{s}*.

## Solved Problem 1

In the following circuit, transform the voltage source of 50V with an internal resistance of 5 Ω into the current source.

To replace the voltage source with the current source,

Thus the circuit becomes,

## Solved Problem 2

For the given circuit, transform the current source into the voltage source.

In the given problem, current source I = 15 A and R_{s} = 10 Ω.

To replace the current source with the voltage source,

So the transformed circuit becomes,

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