by Andrew G. Bell
abell118@ivytech.edu
(260) 481-2288
Lecture 5
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CHAPTER 5
Parallel Circuits
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Parallel Circuit Characteristics
1. There are two or more paths for
current flow
2. The voltage is the same across all
parallel branches
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A Practical Example
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Parallel Circuit Nodes
• Two types of nodes or connections:
– Dividing Node: A junction where current
enters by one connection but leaves by
two or more connections
– Summing Connection: A junction where
current enters a junction by two or more
connections but leaves via one
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Parallel Circuit Nodes (cont.)
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Parallel Circuit Current
• All branch currents are supplied by the
power supply.
• Current leaving the (–) terminal is the
same current entering the (+) terminal.
• This is referred to as total current (IT).
• The total current equals the sum of the
branch currents.
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Parallel Circuit Current (cont.)
• Since the total current is equal to the
current supplied by the source, the total
current can be stated as:
IT = IR1 + IR2 … + IRn
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Kirchhoff’s Current Law
• Kirchhoff’s current law states that the
sum of the currents entering a junction
must be equal to the sum of the
currents leaving the junction:
Iin = Iout
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Current in a Parallel Circuit
• If the applied voltage (and, therefore,
the voltage across each branch) and the
branch resistance are known, the
current through each branch can be
found by using Ohm’s law.
• The branch with the least resistance
has the most current.
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Total Resistance
• Ohm’s law
method:
VT
RT 
IT
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Conductance Method
1
1
Since G  , GT 
R
RT
1
1
1
Also G1  , G2 
, G3  , etc.
R1
R2
R3
Then GT  G1  G2  G3  ...
And
1
RT 
GT
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Product-Over-The-Sum Method
• This works for a circuit with only two
resistors in parallel:
R1  R2
RT 
R1  R2
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Equal Value Branches
RX
RT 
N
• Where Rx is the value of the branch
resistance and N is the number of
branches
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Reciprocal Method
This works for a circuit with any number of
resistors in parallel:
1
RT 
1
1
1


R1 R2 R3
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Assumed Voltage Method
1. Assume a supply voltage (VT)
2. Calculate all branch currents
3. Add branch currents to find IT
4. Find RT by applying Ohm’s law:
VT
IT
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Example
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Total Resistance
Important Concept
• The total resistance of parallel circuits is
always less than the smallest value
branch resistance.
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Power in Parallel Circuits
1. Summation method
PT = PR1 + PR2 … + PRn
2. Ohm’s law method PT  I T  VT
PT  I T  RT
2
2
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VT
PT 
RT
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Opens in Parallel Circuits
1. If a branch opens, the current goes to
zero in that branch.
2. If the total current decreases, the total
resistance increases.
3. Branch voltage remains the same
across the open branch and the other
branches.
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A Practical Example
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Shorts in Parallel Circuits
• Remember: There are 0 across a short.
• The branch resistance goes to 0; thus, the
total resistance goes to 0.
• Since there are 0 across the branches, no
voltage drop is developed.
• A protective device is required because
current is maximized.
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Contrasting Series and
Parallel Circuits
SERIES
•
•
•
•
IT is constant
KVL is used
VT = sum of drops
RT = sum of resistors
PARALLEL
•
•
•
•
IT is the sum of IRn
KCL is used
VT is constant
RT is reciprocal of
the sum of the
reciprocals
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Voltage Sources in Parallel
• Sources are used in parallel to increase
the amount of total current available.
• While VT remains the same, IT
increases by the amount of each
source.
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Current Dividers in a
Two-Branch Circuit
 R2 
I1  
  IT
 R1  R2  
 R1 
I2  
  IT
 R1  R2  
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Current Dividers in a
Two-Branch Circuit (cont.)
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Current Dividers in a
Two-Branch Circuit (cont.)
RT
I1  I T
R1
RT
I 2  IT
R2
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