1. EE2010 Fundamentals of Electric Circuits Lecture 11 Network Theorems: Norton’s Theorem

2. NORTON’S THEOREM Any two-terminal linear d.c. network can be replaced by an equivalent circuit consisting of a current source and a parallel resistor, as shown in Fig.

3. Norton’s Theorem Procedure Preliminary: 1. Remove that portion of the network across which the Norton equivalent circuit is found. 2. Mark the terminals of the remaining two-terminal network. R N : 3. Calculate R N by first setting all sources to zero (voltage sources are replaced with short circuits, and current sources with open circuits) I N : 4. Calculate I N by first returning all sources to their original position and then finding the short-circuit current between the marked terminals. It is the same current that would be measured by an ammeter placed between the marked terminals. Conclusion: 5. Draw the Norton equivalent circuit with the portion of the circuit previously removed replaced between the terminals of the equivalent circuit. NORTON’S THEOREM

4. The Norton and Thévenin equivalent circuits can also be found from each other by using the source transformation NORTON’S THEOREM

5. EXAMPLE - 1 Find the Norton equivalent circuit for the network in the shaded area in Fig.

6. Steps 1 and 2: See Fig. Step 3: See Fig. EXAMPLE - 1

7. Step 4: See Fig. Step 5: EXAMPLE - 1

8. Find the Norton equivalent circuit for the network external to the 9 Ω resistor in Fig. EXAMPLE - 2

9. Solution: Steps 1 and 2: Step 3: EXAMPLE - 2

10. Step 4: Step 5: EXAMPLE - 2

11. Find the Norton equivalent circuit for the portion of the network to the left of a-b in Fig EXAMPLE - 3

12. Solution: Steps 1 and 2: Step 3: EXAMPLE - 3

13. Step 4: (Using superposition) For the 7 V battery For the 8 A source we find that both R1 and R2 have been “short circuited” by the direct connection between a and b, and EXAMPLE - 3

14. Step 5: EXAMPLE - 3

15. Find the Norton equivalent circuit for the network in the shaded area of the network in Fig. Example -4

16. Solution: Steps 1 and 2: Step 3: See Fig. Example -4

17. Step 4: Example -4