Lesson 5: Series-Parallel
Circuits
Learning Objectives

Apply the rules for analyzing series and
parallel circuits to a series-parallel circuit.

Compute the total resistance in a seriesparallel 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.
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
Series - Parallel Circuits
 Complex
circuits
May be separated both series
and/or parallel elements
 Other circuits
Combinations which are neither
series nor parallel
Series - Parallel Circuits

To analyze a circuit
 Identify
elements in series and elements in
parallel:
Series - Parallel Circuits

To analyze a circuit
 Identify
elements in series and elements in
parallel:
RULES FOR ANALYSIS (1)
1. Same current occurs through all series
elements.
2. Same voltage occurs across all parallel
elements.
3. KVL and KCL apply for all circuits, whether
they are series, parallel, or series-parallel.
RULES FOR ANALYSIS (2)
4. Redraw complicated circuits showing the
source at the left-hand side.
5. Label all nodes.
6. Solve the problem…
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
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)
The Series-Parallel Network
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
R234

 





1
1


  4.8
1
1
1
1
1
1

 



 

R

 2 R3 R4   20 30 8 
The Series-Parallel Network
SECOND: Simplify and redraw the circuit
RT  2  4.8  6  12.8 
The Series-Parallel Network
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
 R   50 
R34        25
n  2 
The Series-Parallel Network
R234  R2  R34
 15  25  40
The Series-Parallel Network




1
RT  
  8
 1  1 
 10 40 
Example Problem 1
Determine the Rbc of this network:
Example Problem 2
Determine ITOT, I1, I2, Vad
Example Problem 3
Determine ITOT, I1, I2, Vab
Example Problem 4
Determine the unknown voltages in the network
below:
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)
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.

 RX 
VX  E 

 RT 
 R4 
Vcd  Va 

 R3  R4 
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.
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

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

REQ   20  40  30  20
 REQ 
I X  IT 

 RX 
 20 
I 2  ITOT 

20

40


Example Problem 6
Determine I2 using the CDR. Find Va, Vbc
Example Problem 7
Determine ITOT, I1, Va, Vad