Source Transformation | Source Transformation Technique

By Mona Kumari|Updated : May 4th, 2022

We know that the basic methods of analysis for any electrical network / electric circuit are Nodal analysis & Mesh analysis. 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.

In this article, get an overview of the Source Transformation technique and how to apply this technique while solving the electric circuit/network problem. In this article, we also discussed the example questions based on the Source Transformation technique.

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What is Source Transformation Technique?

The technique/method of transforming the source of one form into the other form is known as the Source Transformation technique. This Source Transformation technique is very much useful for simplifying the networks or circuits, which are having practical sources. 

We know that there are 2 types of practical sources namely, practical voltage source and practical current source. Hence, we can apply the Source Transformation technique for these 2 sources for converting one type into the other. Now, let’s discuss the following two cases one by one by using the Source Transformation technique.

  • 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. Whereas 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.

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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 apply this Source Transformation technique for dependent practical voltage sources also.  

  • 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.   

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.

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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 Example Questions

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

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Solution: Step 1: In the given electric circuit, there are 3 branches. Among which, 2 branches are having 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.

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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.

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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.

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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. 

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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.

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FAQs on Source Transformation

  • No, we can’t apply the source transformation method for ideal sources since the internal resistances of the ideal voltage source and ideal current source are not the same. We must keep the same resistance value while using the source transformation method.

  • Yes. We can apply the source transformation method for the circuits, which are having dependent sources provided the dependent variable is outside the part of the network where we are applying source transformation.

  • Yes. We can apply the source transformation method for converting Thevenin’s equivalent circuit into Norton’s equivalent circuit and similarly for converting Norton’s equivalent circuit into Thevenin’s equivalent circuit since Thevenin’s and Norton’s equivalent circuits resemble practical voltage and current sources. And the internal resistance of both circuits is the same.

  • Yes, we can apply the source transformation method for both practical DC sources and practical AC sources. Similarly, we can apply the source transformation technique for both practical dependent DC sources and practical dependent AC sources.

  • Generally, the source transformation technique will be very much useful for simplifying the given electrical network/circuit. But we can’t apply the source transformation technique for the part of the circuit/network if we are supposed to find the response of a branch, which belongs to the same part of the circuit/network.

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