 Hello everyone, in this video we will be discussing about a linear circuit and try to extract a Thevenin's equivalent out of it where only dependent sources are operating. Here is the learning outcome by the end of this session students will be able to draw a Thevenin's equivalent circuit where only dependent sources are present. Okay, so this is a problem where we only have the presence of dependent sources. We don't have any sort of independent sources here. So let me try to explain you this with a simple example which has a similar analogy. For instance, just imagine that you are a constructor or you are the owner of a plot where you want to construct your own house and you want to raise money for that one. So the simple idea that we generally perform is we go to the bank and get some loan. So this is a scene where you are dependent on the bank for generating this money for the construction of your house. So in case if you want to generate money where there is no bank then probably your entire plans are going to collapse. So this is something like that wherever we have a linear circuit or any sort of electronic circuit if there is a presence of only independent source that's well and fine. We don't have any dependences but in those cases where we have independent as well as dependent sources then the independent source is responsible for generating some sort of voltage or current across the dependent sources. Whereas in the cases which you are able to see on the screen now where only dependent source is present. Now as you can see here we have as you can see here we have dependent source which is 2 times the current. So and this current is nothing but the loop current flowing in the first mesh across the there exist as 5 ohms and 10 ohms. So here the problem is this is dependent on something a current where the current is not present. So in fact this current I should be actually developed by some independent source then there would have been a physical existence of this dependent source. Now let's have a look at what problems we would face in identification of Thevenin's equivalent circuit for the given network. Let's find this. So step number one is to calculate the Thevenin's resistance or Thevenin's voltage whichever you consider to be more compatible with we will be going for that one. Now the problem what we are having here is okay so just by looking at the circuit we can easily say that by observing the circuit I can easily conclude that the value i is equal to 0. The reason is since there are no independent sources since there is no independent source the value i is going to be 0 and when this i is 0 this entire dependent source is going to be 0 okay. So since there is no current the value of i is going to be 0 and hence if I try to calculate this short circuit current in my upcoming step then probably the value of i is going to be 0. And since there is no independent source the value of voltage in the given circuit is also 0. So if I try to calculate the value of RTH similar to what we have seen earlier where we calculated by applying Ohm's law that is VOC by ISC. This is something like 0 upon 0 which is invalid. So this is an invalid operation even in mathematics. So how would we rectify this or how would we tackle with this kind of problems? The only problem that we have here is since there is no independent source voltage and current both are 0 but that does not mean that the value of R is also going to be 0. So this way of calculating the value of RTH by being dependent on VOC and ISC in the absence of independent source is an improper method. So what we can do is we will externally connect a voltage source which will make some current i to pass through that and then we will be identifying the ratio of V upon i to calculate the value of RTH. Since we are applying this one we are aware of how much voltage we are applying. So generally the policy or generally the way or generally the process that we follow is we apply one volt source or unit volt amount of current. So generally the way of performing this is to calculate a unit amount of voltage or a unit amount of current and then consider we have some voltage and current present in the circuit moving into the circuit so that it forms some voltage or current source according to the availability or the type of the dependent source. So generally the method that we follow is we tend to apply a unit amount of voltage source and a unit amount of current or some amount of current is going to flow. So generally the process that we follow for calculation of these kind of dependent source based problems is that we apply a unit volt of source across the output terminals and that will tend to pass some sort of current into the circuit and hence we will be having a knowledge of what V we have applied and what current is flowing into the circuit and based on which we can easily identify the ratio V upon i to calculate the value of RTH. So let us have a look at how we can do this. So in the first step what we are going to do is apply this V and hence some current i is flowing. So having a look at this particular diagram now let us proceed. Now the modified Thevenin's resistance formula is going to be V what we have applied upon the i which is an action of the applied V. So now we will be applying, we will be considering this node as V and let us try to apply kc across this one and see what equation we are getting. So this is going to give us V upon 10 plus this source that is V minus 2i upon 5 is what we are having is V. So on the right side what we are having is current i. So this is our kc equation. Now let us try to solve this based on observation. I can say that the value of i is nothing but it is V upon 10. So I will try to replace that i with V upon 10 and see what I am getting. So finally the value of V that I am getting is something like 13 by 50 is equal to i. So I am interested in the ratio of V upon i therefore the value of V upon i which is nothing but rth as per this particular formula is 13 by 50. So this is the value of rth. So do we have to calculate anything else that is all. So just after this step number one we can directly proceed to the final step of drawing the equivalent circuit where we have the value of rth as 13 by 50 and the value of Vth can be straight away written as 0 volts. So since it is 0 you can either directly draw it as Vth or you can directly show a short circuit which indicates that the Vth voltage is 0 both are one and the same. So when we are specifically talking about identification of a Thevenin's equivalent circuit where there is some sort of dependency. This operation becomes invalid like we have seen in our earlier videos where we have calculated Thevenin's equivalent based on the availability of only independent sources where we have calculated the Thevenin's resistance and Thevenin's resistance independently. So wherever we have the presence of independent and dependent sources both we need to calculate Voc and Isc and then calculate the value of rth by taking the ratio of Voc upon Isc. Whereas in case of a linear network where there is a presence of only dependent voltage source the calculation of Thevenin's resistance by having the ratio of Voc upon Isc is invalid since both the values are going to be 0 and hence we need to calculate the ratio V upon I where we externally apply this voltage. So this as this is an important observation in our case here are the references thank you.