 Welcome. Today we will study Norton's theorem which is to be used to solve circuit and network related problems. Learning outcome at the end of this session students will be able to apply Norton's theorem to basic electronic circuits. Before starting with network theorem that is Norton's theorem, student should recall Critchoff's voltage law, Critchoff's current law, series and parallel combination of passive circuit elements, voltage division, current division, star and delta connection as well as source transformation. Now we will see introduction to Norton's theorem. So basically converse of Thevenian's theorem is Norton's theorem. Instead of equivalent voltage source in case of Thevenian's theorem, here it will consist of equivalent current source. Finding equivalent resistance of source network is same as done in Thevenian's theorem. However in last step to draw Norton's equivalent circuit, equivalent resistance of a source network is kept in parallel with current source. Now we will see statement of Norton's theorem. A linear active network consisting of independent and or dependent voltage or current sources and linear bilateral network elements can be replaced by an equivalent circuit consisting of a current source in parallel with a resistance. The current source being the short circuit current across the load terminal and the resistance being the internal resistance of the source network looking through the open circuited load terminals. So in Norton's theorem, the complicated circuit is to be replaced by equivalent current source in parallel with internal resistance. That internal resistance is similar to Thevenian's resistor and that current is to be called as short circuited current. Now we will see one example related to Norton's theorem to understand how it is working. So this is the example. Find the current in 5 ohm resistor of the circuit shown below. So in the circuit there are two sources that is independent sources. One is voltage source of 10 volt. Another is current source of 1 ampere and the 5 ohm resistor is there. So we have to find out current flowing through this 5 ohm resistor. Now first step is we have to remove 5 ohm resistor and we have to short those two terminals that is x and y and current flowing through that short circuited branch is to be represented by ISC. So this is the first step in Norton's theorem. Now thing is we have to find out ISC short circuit current. So for that we have to assume node voltage V at node 1. There are two nodes node 1 and node 2. Node 2 is reference node and here by applying nodal analysis, first of all we have to find out value of voltage V. So nodal analysis will give you the value of voltage V as given by equation that is V minus 10 volt upon 3 plus V by 6 plus V by 10 minus 1 is equal to 0. So after solving this we get value of node voltage V is equal to 7.22 volts. Next step is to find out ISC we have to apply KVL that is Krichoff's voltage law at the loop and the loop is 1 node 0.1 node 0.x node 0.y and node 0.2. So by applying KVL at this loop the equation we are getting is V minus ISC multiplied by 10 is equal to 0. Value of V we got as 7.22 minus 10 ISC is equal to 0. So from this the value of ISC is equal to 0.722 amperes. Next step is we are going to find out equivalent resistance of source network. So to find Norton's equivalent resistor which is to be reprinted by RNT through XY that 5 ohm resistor is removed and all independent sources are deactivated. So we have to short circuit the branch consisting of 10 volts voltage source and we have to delete the current source of 1 amperes and looking through the XY terminals we can find out RNT. So value of RNT is parallel combination of 3 ohm resistor with 6 ohm resistor and this combination is in series with resistor of 10 ohm. So RNT is given by 3 parallel 6 plus 10. So from this we get value of RNT is equal to 12 ohms. Now last step in the Norton's theorem is we have to draw Norton's equivalent circuit and across this we have to connect load resistor. In this case the load resistor is to be reprinted by 5 ohm resistor and as we have to find out the value of current flowing through 5 ohm resistor here it is to be reprinted by I5 ohm. So the figure shows equivalent circuit of Norton's theorem. So first here it is current source which is to be reprinted by ISE and its value is 0.722 amperes. In parallel to this current source there is its equivalent internal resistance or Norton's resistance whose value is 12 ohm and across this combination we have to connect or we have to reconnect the resistor of 5 ohm. Now to find out current flowing through resistor of 5 ohms we have to use current division rule. So branch current or current flowing through 5 ohm resistor is I5 ohm. Total current is ISE whose value is 0.722 amperes. So by current division rule I5 ohm is equal to ISE multiplied by RNT upon RNT plus 5. So if we put respective values that is ISE is equal to 0.722 amperes and RNT is equal to 12 ohm we get value of current I5 ohm is equal to 0.5096 amperes. So like this you can solve a problem or you can find out current flowing through a resistor by using Norton's theorem and we have to use 4 steps. Step 1 is you have to remove the resistor and you have to short circuit the branch and current flowing through that short circuited branch is to be reprinted by ISE. We have to find out ISE by conventional network solving methods. After that we have to remove the resistors and looking from that side we have to find out RNT or internal resistance of the source network. To find out internal resistance of the source network we have to deactivate independent sources. Independent voltage source is to be replaced by short circuit and independent current source is to be replaced by open circuit. Last step is we have to draw equivalent network or Norton's equivalent circuit by connecting source current source which is to be reprinted by ISE. Into that we have to connect resistors resistor in parallel and across this combination we have to connect or we have to reconnect load and then by using current division rule you can find out current flowing through respective resistor. The reference which I have used is circuit theory analysis and synthesis by A. Chakraborty. Thank you.