 Hello everyone, welcome to a video lecture on nodal or node analysis in a electrical network. Myself, K. R. Biradar, Assistant Professor, Department of Electronics and Telecommunication Engineering, Walton Institute of Technology, Singapore. Let us start with the learning outcomes first. At the end of this session, you will be able to apply nodal analysis to electrical network and find voltage and currents. These are the contents. Start with introduction, nodal analysis and different points to remember for nodal analysis and there is a concept called super node. And what are the different steps to be followed for nodal analysis, problem and lastly references. Introduction, nodal analysis is based on the Kirchhoff's current law. In this method, one node is assumed as reference node and its potential is assumed to be 0. In nodal analysis, we need to assume one of the node is reference node, its voltage is 0. This node is also called zero potential node or base node or datum node. In the other nodes, the node voltages are measured with respect to base node. These nodes are called major nodes. You can see this diagram. It consists of, there is a reference node, this is also called datum node and B and C are major nodes. These node voltages VB for node B is measured with respect to this datum node and also at node C, the voltage is VC which is measured with respect to this reference node. Common point of all the branches are considered as reference node. The B and C are the major nodes. It is important to note in node analysis, the branch B to E is considered as the entire branch. From here to here, we need to consider as an entire branch, but this A is not another node. Similarly branch C to H is considered as the independent branch, hence node D is not considered as the major node. From C to H, it is an independent branch, hence this node D is not considered to be as a major node. Generally, the nodes where three or more branches meet are the major nodes. You can see this node B will have three branches connected, node C will also have three branches connected. Therefore, these two are the major nodes whereas A and D have connected, only two branches will not be considered as a nodes. In the figure shows the direction of the branch currents and the voltages, node voltages. Node voltages are VB and VC, branch currents are I1, I2, I3 and here I3, I4 and Ix due to this current source. Apply KCL at the nodes, all the outgoing currents are considered to be negative sign. I1 is going out, I2 is also going out, I3 is also going out. Therefore, minus I1, minus I2, minus I3 equal to 0 at node B. Similarly, at node C, I3 is incoming, I4 is outgoing and Ix is incoming. Therefore, I3 plus Ix minus I4 equal to 0. If I want to write currents I2, I3, I4, we need to consider the resistors R2 between B and C. The B node have a voltage VB and node C have voltage VC. If I want to write this I3, I3 equal to it is flowing from node B to C. Therefore, VB is positive and VC is negative, VB minus VC divided by R2. Similarly, current across R3 will be VB minus 0 because this is V equal to 0, a reference node, VB minus 0 divided by R3 that is equal to VB by R3. Now branch across CG, we consider that is current across R4, VC minus 0 divided by R4 that is also equal to VC by R4. Between B and E, we have considered one voltage source. This voltage source also considered while writing the I1, I1 is flowing from B to E, but this voltage source is tries to force current against I1. Therefore, Vx we need to take minus sign. Therefore, I1 equal to VB minus Vx minus 0 that is reference rho divided by the resistance across this is R1. This also equal to VB minus Vx divided by R1. What are the different files to remember while applying the nodal analysis? First one is while assuming branch currents, make sure that each unknown branch current is considered at least once, we need to consider all the branch currents. Second one convert the voltage source present into their equivalent current sources for nodal analysis. If I want to apply these nodal analysis, I need to have only current source that is why convert that voltage source into current source. Second one follows the same sign convention, currents entering at node R to be considered as positive while currents leaving the node R to be considered as negative that means incoming currents to a node are positive and outgoing currents to a node are negative. As far as possible, select the directions of various branch currents leaving the respective nodes. Supernode in the figure the nodes V2 and V3 are directly connected through voltage source without any circuit element between V2 and V3 there is no circuit elements like resistor capacitor inductor instead there is a voltage source. The reason surrounding a voltage source which connects the two node directly is called supernode. This is actually supernode. Now consider a loop including supernode as shown in figure 5. We need to form a loop by using this supernodes and the voltage source. Here V2 and V3 and their sign conventions, now you apply the KVL to the loop. If I apply KVL this minus 2 plus that is plus V2, Vx is plus 2 minus it is minus Vx again V3 is plus 2 minus it is minus V3 that means V2 equal to Vx plus V3 what are the different steps for the nodal analysis. First one identify the nodes and choose the node voltages like V1, V2, V3 etc. Second one choose the currents preferably leaving the node at each branch connected each node. Third one apply KCL at each node with proper sign convention. Third one if there are supernodes obtain the equations directly in terms of node voltages which are directly connected through voltage source just we have we have seen this. Fifth one obtain the equation for the each branch current in terms of node voltages and substitute in the equations obtained in step 3. We need to find the branch currents in terms of node voltage and substitute those in step number 3. Sixth one solve all the equations obtained in step 4 and 5 simultaneously to obtain the required node voltage. Using the equations obtained from 4 and 5 we can find the unknown voltage and the currents. Let us see a problem for the circuit shown find the branch currents I1, I2, I3 and node voltages V1 and V2. This is the electrical circuit having three resistance and the two current sources. We have marked this as V1 and this is V2 these two are the major nodes. There is a reference node here which is connected to ground which value equal to 0. And currents which are leaving from this node is I1 and I2 and from this node it is I3 and 5 ampere. Pause the video and try to solve and find the answer. I think you might have solved this problem let us see the answer. Change node analysis at node 1 or first node what are the currents coming to this node 3 ampere is coming and I1, I2 is leaving plus 3 minus I1 minus I2 equal to 0. At node 2 I2 is coming I3 is leaving and 5 ampere is also leaving I2 minus I3 minus 5 equal to 0. Now I1 equal to that is current across this branch is V1 divided by R that is V1 by 6. Similarly, I2 equal to current is flowing from first node to second node. First node voltage is V1 it is higher potential V1 this is at lower potential minus V2 divided by branch resistance is 3 ohm. Similarly, I3 equal to V2 minus 0 divided by 2 ohm substitute to these I1, I2, I3 in these equations. So, the plus 3 minus I1 is V1 by 6 minus I2 is V1 minus V2 by 3 equal to 0. So, if you simplify it becomes 0.5 V1 minus 0.33 V2 equal to 0. Similarly, at node 2 equation I2 is V1 minus V2 by 3 minus I3 is V2 by 2 equal to 5 is also equal to 0.33 V1 minus 0.83 V2 equal to 0. In these two equations we can find the value of V1 and V2 after finding V1 and V2 we can substitute in these equations we can find the currents I1 I2 I3. The voltage V1 and V2 equal to V1 equal to 2.72 volt and V2 equal to minus 4.9 volt substitute these V1 and V2 will get I1 equal to V1 by 6 which is equal to 0.45 ampere I2 equal to V1 minus V2 by 3 which is equal to 2.54 substitute V1 and V2 will get this answer I3 equal to V2 by 3 which is equal to 2.45 ampere these are the references used to prepare the above ppt thank you.