 Today we are going to study supernode analysis of circuit. So, generally a nodal analysis is used while solving the problems related to circuits, but in some cases it will happen that different condition will arise. So, in such cases other than a normal procedure or the normal theorem we have to implement or we have to use another method to solve a problem. So, today we will see supernode analysis of the circuit. Learning outcome at the end of this session students will be able to apply supernode analysis to find unknown voltages. So, generally supernode analysis is to be used to find unknown voltages present in the circuit. So, before starting with supernode analysis you should pause the video and you should recall how to apply node analysis, what is KVL, KCL, how to apply KVL and KCL. Now, we will move to the topic that is supernode analysis. Friends to study the supernode analysis we are considering a circuit and with the help of that circuit we will understand what actually is supernode analysis is. Generally you can apply node analysis for the circuit and you can find out node voltages. And to solve this you have to use Ohm's law or you have to use KCL and you can solve the problem, but in some cases it will happen that between any two nodes there comes a voltage source. So, in such cases it is difficult to apply node analysis because while applying the node analysis it is very much critical or the node analysis will go wrong. So, instead of applying node analysis we have to use supernode analysis. So, as you can see in a given diagram there are total three nodes node X node Y and node Z. So, to find out the unknown voltages at the nodes we have assigned reference node or ground node here and will apply KCL to these two nodes that is node X and node Y. But in a node analysis you can write the equation for this particular portion of the circuit. So, instead of applying node analysis we have to apply supernode analysis. Now we will see steps to apply supernode analysis. Find total number of nodes for a given circuit. So, we have to find out total number of nodes present in a given circuit. So, in this given circuit there are total three nodes node X node Y and node Z. We will assign it as a node Z. Assign reference nodes and assign voltage designations to non-reference nodes. So, I have assigned a reference node or ground node here and we have to assign designations to the non-reference nodes. So, we will assign VX and VY as a voltage designations to non-reference nodes. Write KCL equation for each node and combine. So, in node analysis what we have done is we will apply KCL Krichov's current flow to the nodes and after writing number of equations and solving these equations we will find out the unknown values. But instead of that here what we have to do is we have to write KCL equations to each node separately and we have to combine those equations. And inside supernode we have to apply KVL that is Krichov's voltage law. And after solving those equations you can easily find out the unknown value of voltages. So, here between node X and node Y there is a voltage of 1 volt. So, this portion of the circuit is called as a supernode. So, what we have to do is we have to write separate equation KCL equation at node X and node Y. We have to combine those two equations and then we have to apply KVL to this portion of the circuit that is node X 1 volt voltage source and node Y. And we have to solve this and then you can find out the unknown values of voltage that is V X and V I. As a example what we do is we will try to find out unknown voltages V 1 and V 2. In this particular circuit you can see here this is node 1 I have assigned and this as a node 2 I have assigned and this is third node, but this node is ground node. So, here you cannot apply node analysis because between node 1 and node 2 there comes a voltage source. So, here we have to apply supernode analysis. So, while applying supernode analysis what we have to do is we have to write separate KCL equation at node 1 and node 2 and then we have to combine those two equations and we have to write a single equation. Then we have to apply KVL at this particular portion of the circuit and then we have to solve the equations and we will get the value of unknown voltages V 1 and V 2. So, I will redraw the circuit and we will solve this current source 1 ampere here also it is 1 ampere resistance 1 ohm here also it is 1 ohm node voltages V 1 and V 2 node 1 and node 2 this is ground node. Now, apply KCL at node 1 KCL at node 1 incoming current I will assign it as a negative and outgoing current I assign it as a positive. So, this is 1 ampere current which is going to node 1 it is considered as a negative and unknown current will consider it as outgoing current. So, in this branch we do not know the direction of current. So, I will assign it as a outgoing current. So, equation is minus 1 plus V 1 upon 1 equal to 0 yes. Similarly, we will apply KCL at node 2 at node 2 also 1 ampere current is incoming current we do not know the current in this particular branch it is which is attached or connected to node 2. So, we will consider it as a outgoing current and we will write down the KCL equation what is KCL? Current at node is equal to 0 summation of all the currents at node equal to 0. So, it is minus 1 plus V 2 by 1 equal to 0 now combine KCL equations we have to combine the KCL equations and we have to write a single equation. So, it is minus 1 plus V 1 by 1 plus V 2 by 1 minus 1 equal to 0. So, it is V 1 plus V 2 is equal to 2 make this as a equation number 1. Now, we have combined the KCL equations now in this particular portion we have to apply KVF. So, I will draw the portion 1 volt here it is V 1 here it is V 2 ground plus minus plus minus here it is V 1 here it is V 2 we have to apply KVL to the loop or KVL to the portion or KVL to the super node. So, what is KVL equation? KVL equation is if we go in a clockwise manner it will be V 1 minus 1 minus V 2 equal to 0. So, it is V 1 minus V 2 equal to 1 will make it as a equation number 2 yes. So, if you add equations 1 and 2 if you add equations 1 and 2 V 2 V 2 get cancelled and a value of V 1 will be 3 upon 2 volts you will get value of V 1 as a 3 by 2 volts. And if you subtract equations 1 and 2 if you subtract equation 1 and 2 you will get value of V 2 as a 1 by 2 volts yes are you getting this? So, what we have done is we have written the KCL equations at node individually then we have combined those equations and to the portion of super node we have written KVL equation here you can write it as a by applying KVL to loop by applying KVL to the loop you can write down the equation V 1 minus 1 minus V 2 equal to 0. And by after solving these two equations you will get value of V 1 as 3 by 2 volts and value of V 2 as a 1 by 2 volts ok. So, this is all related to the super node analysis. While preparing this video lecture I have used circuit theory analysis and synthesis by H. Chakravarty, Dhanpataray publication 6th edition. Thank you.