SeriesParallel Circuits

1
Chapter 7

• Series-Parallel Circuits

2
The Series-Parallel Network

• A branch is any part of a circuit that can be
  simplified as having two terminals.
• The components between these two terminals may be
  any combination of resistors, voltage sources, or
  other elements.
• Many complex circuits may be separated into a
  combination of both series and/or parallel
  elements.
• Other circuits consist of combinations which are
  neither series nor parallel.

3
The Series-Parallel Network

• To analyze a circuit, you must first recognize
  which elements are in series and which are in
  parallel.
• In this circuit, R2, R3, and R4 are in parallel.
• This combination is in series with R1 and R5.

4
The Series-Parallel Network

• In the circuit shown, R3 and R4 are in parallel.
• This combination is in series with R2.
• The entire combination is in parallel with R1.

5
Analysis of Series-Parallel Circuits

• The rules for analyzing series and parallel
  circuits still apply.
• The same current occurs through all series
  elements.
• The same voltage occurs across all parallel
  elements.
• KVL and KCL apply for all circuits, whether they
  are series, parallel, or series-parallel.

6
Analysis of Series-Parallel Circuits

• Redraw complicated circuits showing the source at
  the left-hand side.
• Label all nodes.
• Develop a strategy. It is usually best to begin
  the analysis with the components most distant
  from the source.
• Simplify recognizable combinations of components.

7
Analysis of Series-Parallel Circuits

• Determine the equivalent resistance RT.
• Solve for the total current.
• Label the 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.

8
Analysis of Series-Parallel Circuits

• By putting R2 and R3 in parallel, the circuit
  reduces to a series circuit.
• Use the Voltage Divider Rule to determine Vab and
  Vbc.
• Calculate all currents from Ohms Law.

9
Analysis of Series-Parallel Circuits

• To find the voltage Vab, first redraw the circuit
  in a more simple form.
• The original circuit consists of two parallel
  branches.

10
Analysis of Series-Parallel Circuits

• Vab may be determined from a combination of the
  voltages across R1 and R2.
• Use the Voltage Divider Rule to find these two
  voltages.
• Use KVL to find Vab.

11
Analysis of Series-Parallel Circuits

• To find the currents in the circuit, first redraw
  the circuit.
• Move the source branch all the way to the left.
• Reduce the circuit to a series circuit..

12
Analysis of Series-Parallel Circuits

• Use the Voltage Divider Rule to determine
  voltages.
• Use Ohms Law to determine the currents.

13
Bridge Circuit

• Suppose the circuit has Rx 15 k?.
• We want to determine Vab.
• Redraw the circuit as shown on the next slide.

14
Bridge Circuit

• Use the voltage divider to determine Va and Vb.
• Vab 2.5 V.

15
Bridge Circuit

• Suppose Rx is a short circuit (0 ?).
• Determine VR1 by the Voltage Divider Rule.
• VR2 10 V.
• Vab 8 V.

16
Bridge Circuit

• Suppose Rx is an open.
• Find VR1.
• VR2 0 V (No current flow).
• Vab -2 V.

17
Transistor Circuit

• A transistor is a device that amplifies a signal.
• The operating point of a transistor circuit is
  determined by a dc voltage source.
• We will determine some dc voltages and currents.

18
Transistor Circuit

• Apply KVL
• VBB RBIB VBE REIE
• Using IE 100IB, we find IB 14.3 ?A.
• All other voltages and currents can be determined.

19
Potentiometers

• An example of a variable resistor used as a
  potentiometer is the volume control on a
  receiver.
• When the moveable terminal is at the uppermost
  position, VBC 60 V.
• At the lowermost position, VBC 0 V.

20
Potentiometers

• If a load is added to the circuit, VBC changes.
• At the upper position, VBC 40 V.
• At the lower position, VBC 0 V.