# Electrical Source Conversion (Voltage and Current Sources)

We often need to do electrical source conversion during circuit analysis. Because it makes our effort easier.

We can convert an ideal voltage source with a series resistance, to a current source. In that case, we have to connect the same resistance in parallel with the equivalent current source.

On the other hand, we can convert an ideal current source to a voltage source also. In that case, we connect the parallel resistance of the current source in series with the equivalent voltage source.

### Example of electrical source conversion

Is it a little bit confusing?

Let us go through an example of actual electrical source conversion. See the voltage source below. It is a source of 10 volts. It has a resistance of 5Ω in series with it. Let us connect another 5Ω resistor across the source, terminals A and B as shown below.

Let us now find out the current through the load resistance between A and B. It is 10/(5+5)A or 1A.

After that, we replace the load resistance between A and B with a short circuit path. Now, the current through the short circuit path is 10/5 A or 2A

Now we shall create a current source with this current 2A. Then we connect the resistance 5Ω in parallel.

Finally, we connect the same load resistance of 5Ω across terminals A and B.

Obviously, now 1A current flows through the 5Ω load resistance between A and B.

So, we have observed that the 10V voltage source, as well as the 2A current source, give the same current to the same load resistance.

Undoubtedly, that voltage source and the current source are equivalent to each other. So, we have seen how easily we can perform electrical source conversion.

### Electrical Source Conversion Formula

#### Conversion of  Voltage Source to Current Source

Let us draw a general form of a voltage source.

Here, the emf of the source is V volt. In addition, it has an internal resistance Ri. Without a doubt short circuit current from A to B is

The equivalent current source is

#### Conversion of Current Source to Voltage Source

Let us draw a current source

The open circuit voltage across A and B is

So, the equivalent voltage source has the emf of V volts. The internal resistance Ri now is in series in the source. Obviously, the equivalent voltage source is as shown below.

### Definition of Electrical Source Conversion

We can convert a voltage source to an equivalent current source. For that, the current of the current source is the short circuit current between the voltage source terminals. Furthermore, the internal resistance of the current source will be the same internal resistance of the voltage. Differing from the voltage source, we connect that internal resistance in parallel for the current source. Conversely, we can convert a current source to an equivalent voltage source. At this time, the voltage of the voltage source will be the open circuit voltage of the current source. The internal resistance of the voltage source will be the same internal resistance of the current source. In contrast to the current source, we connect the internal resistance in series in the voltage source.

### Example of Electrical Source Conversion

#### Voltage Source to Current Source Conversion

Let us draw an equivalent current source of the given voltage source.

First, we short circuit terminals A and B. Then the short circuit current is 12/6=2A.

Finally, we draw the converted current source as,

#### Current Source to Voltage Source Conversion

Alternatively, let us convert a current source to its equivalent voltage source.

The open circuit volrage of the current source is 4X3 or 12 Ω. Here, we have connected the internal resistance of 3Ω in series with the source voltage.

These were two very basic examples of electrical source conversion.

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