Superposition Theorem

In this blog I'm here to explain the concept of Superposition Theorem in a way that makes it easy to understand. 

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Introduction:

Imagine you're trying to figure out how much current is flowing through a light bulb in a circuit, but there are multiple batteries (or voltage sources) affecting the current. The Superposition Theorem is a tool that helps us simplify this situation. It tells us that you can break down the overall effect of multiple sources into the sum of their individual effects.

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Step-by-Step Guide to Superposition:

1. What Is Superposition?

   Think of a circuit as a party. Each voltage source (like a battery) is a guest at the party, and they all affect the mood (voltage and current) in the room. Instead of trying to figure out what all the guests are doing at once, Superposition suggests you first focus on one guest at a time.

   • Step 1: You "turn off" all the other guests (sources) except for one.
   • Step 2: See how that one guest (source) affects the mood (voltage/current).
   • Step 3: Repeat the process for each guest (source) one by one.
   • Step 4: Add up all their individual effects to find the total mood (current/voltage).

2. Turning Off Sources:

   When we say "turn off" a source, what do we mean?

   • If we have a voltage source, we replace it with a short circuit. This is just a wire because a short circuit has zero voltage across it.
   • If we have a current source, we replace it with an open circuit. This essentially means there’s no current flow where that source was.

   It's like ignoring the source completely for the analysis, while leaving the rest of the circuit as it is.

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Example:

Let’s consider a circuit with two voltage sources $V_1$ and $V_2$, and a resistor $R$.

1. Turn off $V_2$: To do this, we replace $V_2$ with a short circuit. Now we only have the effect of $V_1$ on the circuit.

   Calculate the current flowing through the resistor $R$ due to $V_1$ alone. You can use Ohm's Law here: $I_1 = \frac{V_1}{R}$.

2. Turn off $V_1$: Now, replace $V_1$ with a short circuit, leaving only $V_2$ active. Calculate the current flowing through $R$ due to $V_2$ alone: $I_2 = \frac{V_2}{R}$.

3. Add the results: Finally, the total current $I_{total}$ through $R$ is the sum of $I_1$ and $I_2$:

   $$I_{total} = I_1 + I_2 = \frac{V_1}{R} + \frac{V_2}{R}$$

This gives you the total current flowing through the resistor due to both voltage sources.

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Why Does It Work?

The key idea is that voltage and current in a linear circuit behave proportionally. This means the effect of one source is independent of the others — so we can analyse them one by one and then combine their effects.

Imagine you're adding up individual contributions to a team project. Each member works on their part, and when you add up all the work, you get the full result. The Superposition Theorem works the same way.

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When to Use It:

Superposition is most useful in circuits with multiple independent sources (voltage or current sources). It helps to:

• Simplify complex circuits with more than one source.
• Calculate current or voltage at specific components without having to deal with all sources at once.

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Things to Remember:

• Only for Linear Circuits: The Superposition Theorem applies when the circuit elements (like resistors, capacitors, inductors) follow linear relationships. This means the current is directly proportional to the voltage (Ohm's Law).

• Significance of "Turn Off" Concept: When you turn off a voltage source, you short-circuit it, and when you turn off a current source, you open-circuit it. It’s as though the source doesn't exist for that moment of analysis.

• Sum of Effects: When adding up the effects from different sources, you do it algebraically. Pay attention to the signs (positive or negative), as they represent the direction or polarity of voltage or current.

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A Quick Recap:

1. In any circuit with multiple independent sources, analyse one source at a time.
2. "Turn off" all other sources — replace voltage sources with short circuits and current sources with open circuits.
3. Find the effect of each source on the circuit (voltage or current).
4. Add up all these effects to get the total voltage or current.

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Final Thoughts:

Superposition is like doing a "step-by-step" analysis of each source and then combining their effects. It gives you a way to simplify complex problems, which is great for understanding how each source contributes to the behaviour of the circuit.

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And that's the Superposition Theorem! Does that make sense? Please let us know your feedback in comments

Article Written and Reviewed by Mirza Asadullah Baig,  M.E(ECE)

Review Date: 12/Jan/2025

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