LAB 3
Gareth Beckham
Brief3SuperpositionTheorem.pptxENGR 2105
Dr. Kory Goldammer
Superposition Theorem
Superposition Theorem - Components
The superposition theorem extends the use of Ohm’s Law to circuits with multiple voltage or current sources.
In order to apply the superposition, all the components must be linear, or “Ohmic”, meaning that the component obeys Ohm’s Law
Yes: Resistors, Capacitors, Inductors
No: Transistors, semiconductor diodes, and electron tubes, Operational Amplifiers. Such components are never bilateral and seldom linear.
Superposition Theorem
The Superposition is useful when we have more than one Voltage Source or more than one Current Source
We will only consider Voltage Sources in this course
This analysis is done by calculating the current contributed by each source, and then adding or subtracting (i.e. taking the Superposition) the currents contributed by each source
7-2: Current Dividers with Two Parallel Resistances
This slide applies to the special case where we have just 2 resistors in parallel
IT is divided into individual branch currents.
Each branch current is inversely proportional to the branch resistance value.
For two (and only 2) resistors, R1 and R2, in parallel:
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7-2: Current Dividers with Two Parallel Resistances
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
The result validates Kirchoff’s Current Law: The sum of the currents entering a node = the sum of the currents leaving a node:
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Determine The Currents going through each resistors
Last time, we analyzed this circuit and determined the total current was 2 Amps. All of the current flows through R1 and R2, so the current in those resistors must be 2 Amps
2A
2A
Determine The Currents going through each resistors
At Point A, the current splits into two branches. The resistance of Branch 1 is R5 = 10Ω. Last time, we determined the resistance of branch 2 was also 10Ω
2A
2A
Determine The Currents going through each resistors
2 Amps enters node A. We can use the current divider to determine the current leaving node A.
2A
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Determine The Currents going through each resistors
Since 1 Amp goes into each branch, we know the currents through R5 and R6 are each 1 Amp. Use the current divider to find the current through the 12 Ohm resistors.
2A
2A
1A
1A
0.5A
0.5A
1A
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Superposition Theorem – Step 1
R1
R2
R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Problem: R3 is the load resistor. Find the the current through
R3 and the voltage across R3
Step 1: Short Voltage Source V2. Find I3
R2
R1
R3
V1
V2
100 W
20 W
10 W
15 V
13 V
Step 1 – Find RT and IT
R1
R2
R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
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Step 1 - Current Divider
R1
R2
R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
Now that we know the total current is 0.141A, we can apply the current divider approach to find the current through Resistors 1 and 2
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Step 1 - Direction of Current through R3
The total current leaves V1 from the positive (top) terminal and passes through R1. It then splits into two branches. The current passing through R3 is going in in the downward direction.
R1
R2
R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
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Problem: R3 is the load resistor. Find the the current through
R3 and the voltage across R3
Step 2: Short Voltage Source V1. Find I3
R2
R1
R3
V1
V2
100 W
20 W
10 W
15 V
13 V
Superposition Theorem – Step 2
Step 2 – Find RT and IT
Step 2: Short Voltage Source V1. Find I3
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Step 2 – Find R3
Step 2: Short Voltage Source V1. Find I3
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Step 2 - Direction of Current through R3
The total current leaves V2 from the positive (top) terminal and passes through R2. It then splits into two branches. The current passing through R3 is going in in the downward direction.
Step 1: Short Voltage Source V2. Find I3
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Case 1: Currents are going in opposite direction. Subtract the smaller from the larger. The direction of the current is the same as the direction of the larger current.
Case 2: Currents are going in the same direction: Add the currents. The resulting current is in the same direction as both currents.
Step 3 Add or Subtract the Currents to Determine R3 for the Original Circuit
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Verify in Multisim
