1. ELECTRICITY & MAGNETISM LECTURE # 7 BY MOEEN GHIYAS

2. TODAY’S LESSON (Series – Parallel Networks – Chapter 7) Introductory Circuit Analysis by Boylested (10 th Edition)

3. Today’s Lesson Contents Introduction – Series-Parallel Networks General Approach Reduce and Return Approach Ladder Networks Voltage Divider Supply (Loaded and Unloaded) Potentiometer Loading

4. Introduction – Series-Parallel Networks Series-parallel networks are networks that contain both series and parallel circuit configurations. A firm understanding of the basic principles is sufficient to begin an investigation of any single-source dc (or multi-sources connected only in simple series or parallel) network having a combination of series and parallel elements or branches.

5. General Approach Take a moment to study the problem “in total” and make a brief mental sketch of the overall approach. Next examine each region of the network independently before tying them together in series-parallel combinations Redraw the network as often as possible with the reduced branches towards source keeping unknown quantities undisturbed or have provision for the trip back to unknown quantities from the source.

6. General Approach Example – For the network of fig, determine the voltages V 1 and V 2 and the current I. Solution: Redraw the circuit By observation. By KVL in right loop. or

7. General Approach Apply KCL at node a

8. Reduce and Return Approach Used with single-source (or multi-sources connected only in simple series or parallel) series- parallel networks. In this analytical approach we first reduce network towards the source.

9. Reduce and Return Approach Reduce network to single element (R T ) towards the source to determine the source current (I S ). Followed by expanding the circuit backwards.

10. Reduce and Return Approach Then find the desired unknowns by expanding the circuit back to original network.

11. Ladder Network Ladder network appears in fig. The reason for the terminology is quite obvious for the repetitive structure Applying reduce and return approach (starting farthest from source)

12. Ladder Network

13. By Current Divider law By Ohm’s Law

14. Voltage Divider Supply (Loaded & Unloaded) Through a voltage divider network such as the one in fig, a number of terminal voltages can be made available from a single supply. The voltage levels shown (with respect to ground) are determined by a direct application of the voltage divider rule. Figure reflects a no load situation due to the absence of any current-drawing elements connected between terminals a, b, or c and ground.

15. Voltage Divider Supply (Loaded & Unloaded) The application of a load can affect the terminal voltage of the supply. 1k Ω

16. Voltage Divider Supply (Loaded & Unloaded) The larger the resistance level of the applied loads compared to the resistance level of the voltage divider network, the lower the current demand from a supply, closer the terminal characteristics are to the no-load levels. 1k Ω

17. Voltage Divider Supply (Loaded & Unloaded) Let us consider the network of fig with resistive loads that are the average value of the resistive elements of the voltage divider network.

18. Voltage Divider Supply (Loaded & Unloaded) The voltage V a is unaffected by the load R L1 since the load is in parallel with the supply voltage E. Thus V a = 120 V, same as the no-load level.

19. Voltage Divider Supply (Loaded & Unloaded) Now remaining load situation create a series-parallel effect R′ 3 = R 3 || R L3 = 30 Ω || 20 Ω =12 Ω. R′ 2 = (R 2 + R′ 3 ) || RL2 = 32Ω || 20Ω = 12.31Ω.

20. Voltage Divider Supply (Loaded & Unloaded) Applying voltage divider law versus 100 V under no-load conditions

21. Voltage Divider Supply (Loaded & Unloaded) Applying voltage divider law versus 60 V under no-load conditions

22. Voltage Divider Supply (Loaded & Unloaded) If the load resistors are changed to the 1kΩ level, the terminal voltages will all be relatively close to the no-load values 1k Ω

23. Voltage Divider Supply (Loaded & Unloaded) Comparing current levels With 20Ω load With 1kΩ 1k Ω

24. Voltage Divider Supply (Loaded & Unloaded) Example – Determine R 1, R 2, and R 3 for the voltage divider supply of fig. Can 2W resistors be used in the design? Solution:For R 3 : Yes! 2W resistor can be used

25. Voltage Divider Supply (Loaded & Unloaded) For R 1 :Apply KCL at node a, Note: V a ≠ V R1 But V R1 = V ab Yes! 2W resistor can be used

26. Voltage Divider Supply (Loaded & Unloaded) For R 2 :Apply KCL at node b, Yes! 2W resistor can be used

27. Potentiometer Loading For the unloaded potentiometer of fig, the output voltage is determined by the voltage divider rule, with R T in the figure representing the total resistance of the potentiometer.

28. Potentiometer Loading When a load is applied as shown in fig (right), the output voltage V L is now a function of the magnitude of the load applied since R 1 is not as shown in fig (left) but is instead the parallel combination of R 1 and R L.

29. Potentiometer Loading If it is desired to have good control of output voltage V L through the controlling dial or knob (Design Parameter), it is advisable to choose a load or potentiometer that satisfies the following relationship:

30. Potentiometer Loading For example, if we disregard eq. and choose a 1MΩ potentiometer with a 100Ω load and set the wiper arm to 1/10 of total resistance, as shown, then which is extremely small compared to the expected level of 1 V.

31. Potentiometer Loading Using the reverse situation of R T = 100Ω and R L = 1 MΩ and the wiper arm at the 1/10 position, as in fig, we find which is the desired voltage i.e. 1/10 of source voltage E = 10V

32. Summary / Conclusion Introduction – Series-Parallel Networks General Approach Reduce and Return Approach Ladder Networks Voltage Divider Supply (Loaded and Unloaded) Potentiometer Loading