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# Source Transformation

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**Source Transformation** technique is very useful for simplifying the networks or circuits with practical sources. Whenever there is a possibility and requirement to apply the Source Transformation technique for the given circuit, then by applying this technique first and then use any of the methods of analysis based on the requirement so that we can solve the network theory problems easily.

This article overviews the Source Transformation technique and how to apply this technique while solving the electric circuit/network problem. This article also discussed the example questions based on the Source Transformation technique.

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Table of content

## Source Transformation Definition

The technique/method of transforming one form’s source into the other is known as the Source Transformation technique.

The basic analysis methods for any electrical network / electric circuit are Nodal analysis & Mesh analysis. There are 2 types of practical sources: practical voltage and current. Hence, we can apply the Source Transformation technique for these 2 sources to convert one type into the other.

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## Source Transformation Techniques

There are two Source Transformation techniques used:

- Practical voltage source into a practical current source
- Practical current source into practical voltage source

**Practical Voltage Source into Practical Current Source**

The practical voltage source is nothing but an ideal voltage source in series with a resistance. A practical current source is nothing but an ideal current source in parallel with resistance. The following figure shows the conversion of a practical voltage source into a practical current source.

In the above figure, the left-hand side circuit is nothing but a practical voltage source. Whereas the right-hand circuit is nothing but a practical current source. Here, we applied the Source Transformation technique for independent practical voltage sources. Similarly, we can also apply this Source Transformation technique for dependent practical voltage sources.

- IS=VSR.
- The resistance value will remain the same in both circuits.
- The voltage at the open circuit terminals of both circuits is the same.
- In both circuits, the current will be the same if the end terminals have shorted each other.

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**Practical Current Source into Practical Voltage Source**

Previously, we converted the practical voltage source into a practical current source by using the Source Transformation technique. Now, let’s apply the Source Transformation technique for converting a practical current source into a practical voltage source. The following figure shows the conversion of a practical current source into a practical voltage source.

In the above figure, the left-hand side circuit is nothing but a practical current source. Whereas the right-hand circuit is nothing but a practical voltage source. Here, we applied the Source Transformation technique for the independent practical current source. Similarly, we can apply this Source Transformation technique for dependent practical current sources also.

- VS=IS R
- The resistance value will remain the same in both circuits.
- The voltage at the open circuit terminals of both circuits is the same.
- In both circuits, the current will be the same if the end terminals have shorted each other.

## Source Transformation Examples

**Question 1-** Using the Source Transformation technique, calculates the voltage, V, of the following electric circuit.

**Solution:**

Step 1: In the given electric circuit, there are 3 branches. Among which, 2 branches have a voltage source in series with Resistor. We know that a voltage source in series with a resistor can be replaced by a current source in parallel to the resistor by using the Source Transformation technique. So, let’s apply the Source Transformation technique for these two branches.

Step 2: In the above circuit, there are 2 current sources, which are connected in parallel. We can add both the current source values since the direction of the current is the same. Similarly, we can represent the equivalent resistor of the parallel combination of two 10 Ω resistors. The simplified equivalent circuit is shown below.

Step 3: By using the Current Division Rule, we can calculate the current (I) flow-through 20 Ω resistor.

I=2.555+20

=>I=0.5 A

Step 4: By using Ohm’s law, we can calculate the voltage (V) across a 20 Ω resistor.

V=(0.5)(20)

=>V=10 volts

**Question 2-** Using the Source Transformation technique calculates the voltage, V of the following electric circuit.

**Solution: **

**Step 1:** We know that a current source in parallel with the resistor can be replaced by a voltage source in series with the resistor by using the Source Transformation technique. So, we can apply the Source Transformation technique for the right-hand side part of the given circuit. But, we shouldn’t apply the Source Transformation technique for the left-hand side of the given circuit because we have to calculate the voltage across 1 Ω resistor, which belongs to the same part of the circuit.

**Step 2:** Now, write the Nodal equation.

-2+V/1+(V+5)/2=0

=> -4+2V+V+5=0

=> 3V=-1

=>V=-1/3 volts

In this article, we discussed the Source Transformation technique for practical independent DC sources, and then we solved the example questions based on the Source Transformation technique. Similarly, we can apply the Source Transformation technique for dependent DC sources, for practical independent & dependent AC sources also.