1. Lesson 5: Series-Parallel Circuits

2. Learning Objectives
Apply the rules for analyzing series and parallel circuits to a series-parallel circuit.
Compute the total resistance in a series-parallel circuit.
Analyze series-parallel circuits for current through and voltage across each component.
Analyze the power dissipated by each element in a series parallel circuit and calculate the total circuit power.

3. Series - Parallel Circuits
Branch:
Part of a circuit that can be simplified into two terminals (2 nodes).
A node is the point of connection between two or more branches.
Components between these two terminals: Resistors, voltage sources, or other elements

4. Series - Parallel Circuits
Complex circuits
May be separated both series and/or parallel elements
Other circuits
Combinations which are neither series nor parallel

5. Series - Parallel Circuits
To analyze a circuit
Identify elements in series and elements in parallel:

6. Series - Parallel Circuits
To analyze a circuit
Identify elements in series and elements in parallel:

7. RULES FOR ANALYSIS (1)
Same current occurs through all series elements.
Same voltage occurs across all parallel elements.
KVL and KCL apply for all circuits, whether they are series, parallel, or series-parallel.

8. RULES FOR ANALYSIS (2)
4. Redraw complicated circuits showing the source at the left-hand side.
5. Label all nodes.
6. Solve the problem…

10. It will help… Develop a strategy
Best to begin analysis with components most distant from the source
Simplify recognizable combinations of components
Determine equivalent resistance RT

11. It will help… Solve for the total current
Label polarities of voltage drops on all components
Calculate how currents and voltages split between elements in a circuit
Verify your answer by taking a different approach (when feasible)

12. The Series-Parallel Network

13. The Series-Parallel Network
FIRST: Identify elements in series and elements in parallel
20Ω, 30Ω, and 8Ω are in parallel
This parallel combination is in series with 2Ω and 6Ω

14. The Series-Parallel Network
SECOND: Simplify and redraw the circuit

15. The Series-Parallel Network

16. The Series-Parallel Network
In this circuit
R3 and R4 are in parallel
Combination is in series with R2
Entire combination is in parallel with R1

17. The Series-Parallel Network

18. The Series-Parallel Network

19. Example Problem 1
Determine the Rbc of this network:

20. Example Problem 2
Determine ITOT, I1, I2, Vad

21. Example Problem 3
Determine ITOT, I1, I2, Vab

22. Example Problem 4
Determine the unknown voltages in the network below:

23. Solution Steps Determine equivalent resistance RT
Solve for the total current IT
Label polarities of voltage drops on all components
Calculate how currents and voltages split between elements in a circuit
Verify your answer by taking a different approach (when feasible)

24. Common Mistakes Applying VDR
E in the VDR is the voltage across JUST the series elements
Rtotal refers to just the combination of the resistors that are series that you know the total voltage across.

25. Example Problem 5
Determine the voltage drop across the R4 resistor (Vcd) using the VDR. Determine power dissipated by each resistor and verify total power = sum of all power dissipated.

26. Power Calculations
To calculate the power dissipated by each resistor, use either VI, I2R, or V2/R
Total power consumed in a Series-Parallel Circuit is the sum of the individual powers
Compare with IT2RT

27. Common Mistakes Applying CDR
REQ refers to just the combination of the resistors that are in parallel that you know the total current through.
Not using all impedances in the branch

28. Example Problem 6
Determine I2 using the CDR. Find Va, Vbc

29. Example Problem 7
Determine ITOT, I1, Va, Vad