Network theorem part 1

Thevenin theorem and Norton theorem

1. Network Theorem Part-1 Harsha Singh Bais Assistant Professor Department of Physics and Electronics Shri Shankaracharya Mahavidyalaya , Bhilai 1 Network Theorem

2. Outlines Introduction Thevenin Theorem Norton Theorem 2 Network Theorem

3. Introduction Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values Definitions Component A device with two or more terminals into which, or out of which, current may flow Node A point at which terminals of more than two components are joined. A conductor with a substantially zero resistance is considered to be a node for the purpose of analysis. Branch The component(s) joining two nodes. Mesh A group of branches within a network joined so as to form a complete loop such that there is no other loop inside it . Port Two terminals where the current into one is identical to the current out of the other. Circuit A current from one terminal of a generator , through load component(s) and back into the other terminal. An electrical circuit is a path in which electrons from a voltage or current source flow Network Theorem 3

4. Thevenin Theorem A linear network consisting of a number of voltage sources and resistances can be replaced by an equivalent network having a single voltage source called Thevenin’s voltage ( Vth ) and a single resistance called Thevenin’s resistance ( Rth ) Thevenin voltage is obtained at the terminal with open circuit Thevenin resistance is obtained by replacing all the voltage sources by a short circuit. Thevenin voltage and Thevenin resistance are connected in series with the load resistance Total load current is calculated by Network Theorem 4

5. Analysis of Thevenin theorem Network Theorem 5 Consider a network or a circuit as shown. Let E be the emf of the cell having its internal resistance r = 0 and RL load resistance across AB . To find Vth : The load resistance RL is removed and the circuit is opened. The current I in the circuit will be according to the Kirchoff second law for closed loop then I=E/R1+R2 The voltage across AB = Thevenin’s voltage Vth . The voltage across AB will be equal to voltage at R2 Vth =IR 2 then Vth =ER 2 / R 1 +R 2

6. Analysis of Thevenin theorem Network Theorem 6 To find Rth : The load resistance RL is removed. The cell is disconnected and the wires are short as shown.     The effective resistance across AB = Thevenin’s resistance Rth . [ R1 is parallel to R 2 and this combination in series with R3 ]

7. Network Theorem 7 Thus, to find the load current I L , V th and R th are connected in series This proves the Thevenin Theorem

8. Norton Theorem A linear active network consisting of the independent or dependent voltage source and current sources and the various circuit elements can be substituted by an equivalent circuit consisting of a current source in parallel with a resistance. The current source being the short-circuited current across the load terminal and the resistance being the internal resistance of the source network. Norton’s theorem  is the converse of Thevenin’s Theorem Network Theorem 8

9. Network Theorem 9 Step 1 –  Remove the load resistance of the circuit. Step 2 –  Find the internal resistance R int  of the source network by deactivating the constant sources.

10. Network Theorem 10 Step 3 –  Short the load terminals and find the short circuit current I SC  flowing through the shorted load terminals using conventional network analysis methods.

11. Network Theorem 11 Step 4 –  Norton’s equivalent circuit is drawn by keeping the internal resistance R int  in parallel with the short circuit current I SC and find the current through it known as load current I L. I L  is the load current I sc  is the short circuit current R int  is the internal resistance of the circuit R L  is the load resistance of the circuit This is all about Norton’s Theorem.

12. Network Theorem 12 THANK YOU