Superposition theorem states that in any linear, bilateral network where more than one source is
present, the response across any element in the circuit is the sum of the responses obtained from
each source considered separately. In contrast, all other sources are replaced by their internal
resistance. Let us know more about the superposition theorem, solved examples and limitations.
Table of Contents:
What is Superposition Theorem?
How to Apply Superposition Theorem?
Superposition Theorem Solved Example
Limitations of Superposition Theorem
Frequently Asked Questions – FAQs
What is Superposition Theorem?
The superposition theorem is a circuit analysis theorem used to solve the network where two or
more sources are present and connected.
Superposition theorem states the following:
“In any linear and bilateral network or circuit having multiple independent sources, the response
of an element will be equal to the algebraic sum of the responses of that element by considering
one source at a time.”
To calculate the individual contribution of each source in a circuit, the other source must be
replaced or removed without affecting the final result. This is done by replacing the voltage
source with a short circuit. While removing a voltage source, its value is set to zero. When
removing a current source, its value is set to infinite. This is done by replacing the current source
with an open circuit.
The superposition theorem is very important in circuit analysis because it converts a complex
circuit into a Norton or Thevenin equivalent circuit.
Guidelines to keep in mind while using the superposition theorem
When you sum the individual contributions of each source, you should be careful while
assigning signs to the quantities. It is suggested to assign a reference direction to each
unknown quantity. If a contribution from a source has the same direction as the reference
direction, it has a positive sign in the sum; if it has the opposite direction, then a negative
sign.
All the components must be linear to use the superposition theorem with circuit currents
and voltages.
It should be noted that the superposition theorem does not apply to power, as power is not
a linear quantity.
How to Apply Superposition Theorem?
The first step is to select one among the multiple sources present in the bilateral network.
Among the various sources in the circuit, any one of the sources can be considered first.
Except for the selected source, all the sources must be replaced by their internal
impedance.
Using a network simplification approach, evaluate the current flowing through or the
voltage drop across a particular element in the network.
The same considering a single source is repeated for all the other sources in the circuit.
Upon obtaining the respective response for individual source, perform the summation of
all responses to get the overall voltage drop or current through the circuit element.
Superposition Theorem Solved Example
Let us understand how to use the superposition theorem to analyze circuits with the help of an
example.
Example 1: Find the current flowing through 20 Ω using the superposition theorem.
Solution:
Step 1: First, let us find the current flowing through a circuit by considering only the 20 V
voltage source. The current source can be open-circuited, hence, the modified circuit diagram is
shown in the following figure.
Step 2: The nodal voltage V1 can be determined using the nodal analysis method.
The nodal equation at node 1 is written as follows:
The current flowing through the 20 Ω resistor can be found using the following equation:
Substituting the value of the V1 in the above equation, we get
I1 = 0.4 A
Therefore, the current flowing through the 20 Ω resistor to due 20 V voltage source is 0.4 A.
Step 3: Now let us find out the current flowing through the 20 Ω resistor considering only the 4
A current source. We eliminate the 20 V voltage source by short-circuiting it. The modified
circuit, therefore, is given as follows:
In the above circuit, the resistors 5 Ω and 10 Ω are parallel to each other, and this parallel
combination of resistors is in series with the 10 Ω resistor. Therefore, the equivalent resistance
will be:
Now, the simplified circuit is shown as follows:
The current flowing through the 20 Ω resistor can be determined using the current division
principle.
Substituting the values, we get
Therefore, the current flowing through the circuit when only 4 A current source is 1.6 A.
Step 4: The summation of currents I1 and I2 will give us the current flowing through the 20 Ω
resistor. Mathematically, this is represented as follows:
I = I1 + I2
Substituting the values of I1 and I2 in the above equation, we get
I = 0.4+1.6 = 2 A
Therefore, the current flowing through the resistor is 2 A.
Limitations of Superposition Theorem
The theorem does not apply to non-linear circuits. The requisite of linearity indicates that
the superposition theorem is only applicable to determine voltage and current but not
power. Power dissipation is a nonlinear function that does not algebraically add to an
accurate total when only one source is considered at a time.
The application of the superposition theorem requires two or more sources in the circuit.
Frequently Asked Questions – FAQs
Q1
What is the superposition theorem?
Superposition theorem is a circuit analysis theorem that is used to solve the network where two
or more sources are present and connected.
Q2
Is the superposition theorem valid for AC circuits?
The superposition theorem is valid for AC circuits.
Q3
Is the superposition theorem applicable to power?
The requisite of linearity indicates that the superposition theorem is only applicable to determine
voltage and current, but not power. Power dissipation is a nonlinear function that does not
algebraically add to an accurate total when only one source is considered at a time.
Q4
Can the superposition theorem be applied to non-linear circuits?
No, the superposition theorem can only be applied to non-linear circuits.
Q5
Why do we use the superposition theorem?
The superposition theorem is very important in circuit analysis because it converts a complex
circuit into a Norton or Thevenin equivalent circuit.
Superposition Theorem
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5 Jun 2023 — The superposition theorem is a circuit analysis theorem used to solve the network
where two or more sources are present and connected.
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What is the superposition theorem?
AI Overview
The superposition theorem simplifies the analysis of circuits with multiple independent sources
by stating that the response (voltage or current) in any element is the sum of the responses
caused by each source acting alone, with other sources replaced by their internal resistances. This
means you can analyze the circuit with one source at a time and then combine the results to find
the overall response.
Explanation:
1. 1. Linear and Bilateral Circuits:
The theorem applies to linear and bilateral circuits, meaning circuits where the
relationship between voltage and current is linear (described by Ohm's law or similar
equations) and the circuit components behave the same regardless of the direction of
current flow.
2. Multiple Independent Sources:
The theorem is particularly useful when a circuit has more than one independent voltage or
current source.
3. Replacing Sources:
To apply the theorem, you analyze the circuit with one source at a time. When considering one
source, you deactivate the others by replacing voltage sources with short circuits (0V) and
current sources with open circuits (0A).
4. Summing the Responses:
After analyzing the circuit with each source individually, you sum the individual responses
(voltages or currents) to find the overall response in the circuit element.
4.
Example:
Imagine a circuit with a voltage source and a current source. To find the voltage across a resistor
using superposition:
1. 1. Consider the voltage source:
Deactivate the current source (open circuit). Calculate the voltage across the resistor due
to the voltage source
2. Consider th
e current source:
Deactivate the voltage source (short circuit). Calculate the voltage across the resistor due to the
current source alone.
3. Sum the voltages:
Add the voltages calculated in steps 1 and 2. The result is the total voltage across the resistor.
3.
Advantages:
Simplifies Complex Circuits:
By breaking down a complex circuit into simpler ones, superposition makes analysis
more manageable.
Insight into Circuit Behavior:
It helps understand the contribution of each source to the overall circuit response.
This video explains the superposition theorem with an example:
Superposition formula:
According to the superposition principle, the resulting wave y(x,t) will be the sum of these individual
waves: Superposition Formula y(x,t)=y 1 (x,t)+y 2 (x,t)=Asin(kx−ωt)+Asin(kx+ωt) Using trigonometric
identities (sum-to-product formula), the sum of these two waves is: y(x,t)=2Asin(kx)cos(ωt)
