Source transformation in network analysis

 
 Hey friends welcome to the new post of all about electronics and today  we will see the source transformation in  the network analysis. so this is very  useful technique in solving the problems  with the network analysis using this   source transformation we can simplify any circuit in the network in the  network analysis. 

    So as its name suggests  it is related to the source and the  source is here nothing but voltage and  the current. So, using this source  transformation we can convert any  voltage source into the current source  for a vice versa any current source into  the voltage source.So, let's say we have  one voltage source Vs with a series  resistance R, which is connected to a some  network via terminal AB. So using this  source transformation we can convert  this voltage source into the current  source Is with the same resistance R in  a parallel with this current source.  

    Likewise if we have a current source Is  with resistance R in a parallel in  any network then that can be converted   into the voltage source Vs with the same resistance R in a series with this  voltage source. So, here during the  transformation the characteristic of the  network not get changed that means the  voltage across this terminal AB and the  current that is entering into this node  A will remain the same after the  transformation. So, let's say that voltage  across these two terminal AB is Vx and  the current that is entering into this  node a is Ix. So, we can write  Vx= Vs-(Ix*R). That is drop across this resistance R.

      Similarly for the transform network,  voltage across these two terminal will  remain the same that is Vx. And the  current that is entering into this node A  will remain the same, that is Ix after the  transformation. So here we can write V X   is nothing but drop across this resistor R. Let's say that is(I*R). where  current I is the current that is flowing  through this resistor R. So here I is  nothing but Is-Ix. So, we can write  V X as (Is-Ix)*R. That is  nothing but
 Vx= Is*R - Ix*R .  
 Now here we can compare these two equations. So we will get  
Vs- Ix*R=Is*R- Ix*R  
So, this two term will  cancel out. So we will get 
 Vs=Is*R  or we can write  Is=Vs/R  

    So, here in this way we  get a relationship between the voltage  and the current. So, if we have a voltage  source Vs with a series resistors R in  a network that can be transformed into  the current source Is with the same  resistance R in parallel with this  current source. And the value of this current   source will be nothing but Vs/R Let us take one example let's say we  have a 30 volt voltage source with  resistance of 10 ohm in series that is connected to a some Network so we can transform this voltage source  into the current source with the same 10  ohm resistor in a parallel with its  current source.

    So, the value of this  current source I will be given as V/R  Tthat is nothing but a 3 ampere.So in  this way we can transform this 30 Volt  voltage source into a 3 ampere current   source with a 10 ohm resistor in a parallel. Likewise, let's say we have a  current source Is with a resistance R in  a parallel in any network that can be  transformed into the voltage source Vs  with the same resistor R in a parallel.

     The value of this voltage source Vs is  nothing but Is*R. so let us take  one example. Let's say we have a 1A  current source with 10 ohm resistor  in a parallel. So we can transform this  current source into the voltage source  with the same 10 ohm resistor in a  series with this voltage source.  The value of this voltage source V is given  by I*R that is nothing but 10 volt  So, in this way we can transform this 1  ampere current source into the 10 V   voltage source. So, now let's take a one numerical and find the usefulness of  this source transformation in  simplifying the circuit.So, here we have  a one circuit.

    And in this circuit we need to find a  voltage across this 2 ampere current  source. Let's say the voltage across this  2 ampere current source is Vx. We  need to find the voltage across this 2  ampere current source. So just by looking  at the circuit it looks bit complicated  find a voltage across this 2 ampere  current source. But we will see that  using the source transformation we can  easily find out the voltage across this 2 ampere current source.

     So, first of all, let's just concentrate on this left   portion of the circuit. Here we have a  volt voltage source which is connected  the 6 ohm resistor in a series. So we can transform this voltage source into the   current source so that we have a this   ohm resistor and 12 ohm resistor arein a parallel. So, first of all, let's just transform this 4 volt voltage source   into the current source. 

    So, in the equivalent circuit we will have a   current source with a same 6 oh resistor in a parallel. And the value of   this current source I is nothing but V upon R that is 4/6 that is 2 by 3 ampere.So, in this way we can transform this 4V voltage source into these 2 / 3 ampere current  source. so we will have a  2 / 3  ampere current source with a 6 ohm resistor in a parallel in the equivalent  circuit. So, now here as you can see now   we have this 6 ohm resistor and 12 resistors are in a parallel. So, here the  equivalent resistance is let us say Rp  and it is given by 6 ohm in parallel with 12  ohm that is nothing but (6*12)/(6+12)  which is nothing but a  4 ohm. 

    Here we can replace these two  resistance by their equivalent parallel  resistance. So the equivalent circuit now  will have a 2/ 3 ampere current source  is the 4 ohm resistor in a parallel. so   now here again as you can see we can transform this current source into the  voltage source so that we have this 8  volt voltage source with this  transformed voltage source in a series.   So, now let's convert this current  to the voltage source. So, here now we have a 2 /3 ampere current source with  4 ohm resistor in a parallel. So, they're  equivalent transform source will have a  voltage source with 4 ohm resistor in a series.

     And the value of this voltage  source V is given by I*R. That is 2   by 3 into 4 ohm.That that is nothing but 8 by 3 volt. So we can replace this 2 by 3 ampere current source into this 8 by 3 word voltage source.And the equivalentcircuit now we'll have a 8 by 3 volt  voltage source with 4 ohm resistor in a  series that is connected to this 8 volt  voltage source.So, now here we have this 8/3 volt voltage source in series  with this 8 volt voltage source. so we  can replace it with a single equivalent  voltage source so we will have now  8+8/3 that is 32 / 3 volt. 

         We can replace these two voltage sources by  this 32 / 3 volt voltage source. So the  equivalent circuit now will look like  this. Now we have this 32/ 3 volt  voltage source in series with this for ohm resistor. So, here again now we can  convert this voltage source into the  current source so that this 4 ohm and 12  register will come in parallel. And we can  simplify this circuit. so here this 32/3   volt voltage source can be converte  into the current source with this 4 ohm resistor in a parallel.And the value of the  current source I is nothing but V upon R that is (32 /3)/4. which comes  out to be a 8 / 3 A. So, we can replace  this voltage source with their  equivalent current source.


       And the equivalent current equivalent circuit now will look like this. It has a  8 / 3 ampere current source with 4 ohm  resistor in a parallel. So as you can see  now we have the 4 ohm and 12 ohm resistor  are in a parallel. so we can replace  these two registers by their equivalent  parallel resistance. Let's say it is Rp  and it is given by 4 ohm parallel 12 ohm  that is nothing but (4*12)/(4+12)  which comes out to be a 3 ohm  so we can replace these two resistors by  their equivalent parallel resistance 3 ohm. 
  

    Now the circuit will have a 3 ohm  resistor in parallel with this two  current sources. And the voltage across  these 2 ampere current source is nothing  but the voltage drop across this 3 ohm  resistor. So, Vx can be given as 3 * I  where I is nothing but a current that is  passing through this 3 ohm resistor. so  value of I is given as 2 ampere minus 8/3  ampere. And  it comes out to be a - 2/3  ampere. so we can write this I as  - 2/3 ampere.So we will VX =-2 volt  So, in this way  using the source transformation we can  easily simplify any circuit and find the  parameters in the any circuit. 

    So I hope you understood what is source transformation and how it is useful in simplifying the any network or circuit the link is provided in the description below to download more such examples based on the source transformation and if you want the solution for the same please let me know in the comment section below.

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