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Electronics
ParallelResistive
CircuitsPart 1
Copyright © Texas Education Agency, 2014. All rights reserved.
What is a Parallel Circuit?
A parallel circuit is a circuit with more than one path for current flow
This type of circuit is very common This is the type of circuit that is used to deliver
power to an outlet in your home Circuit analysis in a parallel circuit starts the
same way as a series circuit—with Kirchhoff’s Laws
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Review of Kirchhoff’s Law’s
Voltage law- the sum of all voltages in a closed loop is equal to zero The sum of the voltage drops equals the sum of the
voltage sources All of the voltage is always used in a loop
Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node The current into a conductor is the same as the
current out of the conductorCopyright © Texas Education Agency, 2014. All rights reserved.
The Simplest Parallel Circuit
Here is an example of the simplest parallel circuit
This circuit has a power supply and two paths for current flow
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The Simplest Parallel Circuit
The two resistors are different loads
Load one is labeled R1 and load two is labeled R25
R1 R2VS
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Paths for Current Flow
Path One
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R1 R2VS
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Paths for Current Flow
Path Two
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R1 R2VS
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Paths for Current Flow
Path Two
Now let’s apply Kirchhoff’s Voltage Law to each path
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R1 R2VS
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Voltage in Parallel Circuits
Path One- place polarities for the two components
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R1 R2VS
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Kirchhoff’s Law in Parallel Circuits
Path One- place polarities for the two components
In a path for current flow from one side of the battery to the other, the sum of the voltage in a closed loop equals zero
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R1 R2VS
Copyright © Texas Education Agency, 2014. All rights reserved.
Kirchhoff’s Law in Parallel Circuits
Path One- start from the top of the battery, and read polarities going into each component
+ VS – VR1 = 0 or VS = VR1
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R1 R2VS
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Kirchhoff’s Law in Parallel Circuits
Path Two
+ VS – VR2 = 0 or VS = VR2
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R1 R2VS
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Voltage in Parallel Circuits
This is the first equation for a parallel circuit
This equation says that the voltage in each parallel path is the same
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R1 R2
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VS = VR1 = VR2
VS
Current in a Parallel Circuit
Both paths exist at the same time The current that flows through R1 does not
flow through R2
The current that flows through R2 does not flow through R1
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R1 R2
Copyright © Texas Education Agency, 2014. All rights reserved.
VS
Current in a Parallel Circuit
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R1 R2VS
Copyright © Texas Education Agency, 2014. All rights reserved.
Each current is separate and independent To calculate each current flow, use Ohm’s Law
I1 = I2 =
Current in a Parallel Circuit
I1 = , I2 = Apply Kirchhoff’s Current Law to this circuit
Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node
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Copyright © Texas Education Agency, 2014. All rights reserved.
R1 R2VS
Current in a Parallel Circuit
A node is where current splits or combines It is a junction or branching point for current
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R1 R2
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VS
Current in a Parallel Circuit
A node is where current splits or combines It is a junction or branching point for current
Here are the nodes
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R1 R2
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VS
Current in a Parallel Circuit
Current combines or comes back together here
Current splits apart here
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R1 R2
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VS
Water Flow Equivalent
Here is a picture showing the same effect using water flow in a pipe
Water flow here is the same as water flow here
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Water Flow Equivalent
Here is a picture showing the same effect using water flow in a pipe
Flow splits into two parts here
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Water Flow Equivalent
Here is a picture showing the same effect using water flow in a pipe
These two points are the equivalent of an electrical node or junction Where flow splits and then comes back together
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Current in a Parallel Circuit
There are actually three different currents
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R1 R2
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VS
Current in a Parallel Circuit
There are actually three different currents Here is I1
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R1 R2
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VS
Current in a Parallel Circuit
There are actually three different currents Here is I1
Here is I225
R1 R2
Copyright © Texas Education Agency, 2014. All rights reserved.
VS
Current in a Parallel Circuit
Here is IT (total current)
IT is the current leaving and entering the battery 26
R1 R2
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VS
Water Flow Equivalent
Here is the picture using current flow symbols
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IT ITI2
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Current in a Parallel Circuit
From Kirchhoff’s Current Law
IT = I1 + I2
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R1 R2IT
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VS
Current in a Parallel Circuit
From Kirchhoff’s Current Law
This is the second parallel circuit equation
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R1 R2IT
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IT = I1 + I2VS
Start with the equation for parallel circuit current
Using Ohm’s Law, substitute for current I = so
Recall the voltage rule in a parallel circuit
Substitute this rule into the previous equation
Resistance in a Parallel Circuit
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IT = I1 + I2
VS = VR1 = VR2
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IT = , I1 = , I2 = = +
Resistance in a Parallel Circuit
After substitution
VS is the same in each term so it divides out, giving us the following formula for resistance in a parallel circuit
This is the third parallel circuit equation
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= +
Parallel Circuit Equations
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IT = I1 + I2 VS = VR1 = VR2
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For two resistors
Parallel Circuit Equations
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(current adds)
(voltage is the same)
(resistance is more complex,but it basically divides)
Copyright © Texas Education Agency, 2014. All rights reserved.
IT = I1 + I2 VS = VR1 = VR2
Parallel Circuit Equations
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(current adds)
(voltage is the same)
(resistance is more complex,but it basically divides)
Copyright © Texas Education Agency, 2014. All rights reserved.
These three formulas (plus Ohm’s Law)form a “tool kit” to analyze parallel circuits.
IT = I1 + I2 VS = VR1 = VR2
Understanding Resistance in a Parallel Circuit
Resistance looks a little more complicated, so let’s examine it more closely
Consider the following circuit
Each switch is open; each light is off
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S1 S2 S3
L1 L2 L3
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VS
Understanding Resistance in a Parallel Circuit
Close S1 and L1 comes on We get current I1 from the battery Each light is identical
Total current = I1 , total resistance = R136
VSS1 S2 S3
L1 L2 L3
Copyright © Texas Education Agency, 2014. All rights reserved.
Understanding Resistance in a Parallel Circuit
Next close S2 and L2 comes on We get additional current I2 from the battery Total current = I1 + I2, double the current
This means total resistance must be cut in half compared to the previous circuit
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S1 S2 S3
L1 L2 L3
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VS
Do the Math
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Use the following formula
Assume R1 = R2 = 30 Ω
= = .0333 + .0333 = 15 Ω
Example Problem 1
For the following circuit, calculate RT and IT
Begin by writing down the equations we need Start with the formula for RT. Once we calculate
that, we can solve for IT 39
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R1 =300 Ω R2 =200 Ω VS =15 V
Example Problem 1
For the following circuit, calculate RT and IT
Begin by writing down the equations we need40
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R1 =300 Ω R2 =200 Ω VS =15 V
and IT =
Example Problem 1
41
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=
Example Problem 1
42
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= 0.00333 + 0.005 = 0.00833 =
=
Example Problem 1
43
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RT = 120 Ω = 0.00333 + 0.005 = 0.00833
= =
Example Problem 1
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Copyright © Texas Education Agency, 2014. All rights reserved.
RT = 120 Ω = 0.00333 + 0.005 = 0.00833
= =
IT = =
Example Problem 1
45
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RT = 120 Ω = 0.00333 + 0.005 = 0.00833
= =
IT = = = .125 A