Superposition (Circuits for Beginners #13)

Summary

This video explains the concept of superposition in linear circuits, highlighting its application in simplifying circuit analysis. Superposition allows for isolating the effects of each voltage source in a circuit with multiple sources, helping to calculate currents more efficiently. The process involves 'zeroing' out other voltage sources to see their individual contributions. Through an example with a 3V and 6V source, the video demonstrates how superposition can be used to allocate current between different sources. This method is powerful for analyzing complex circuits, but it only works with linear circuit elements like resistors, not non-linear ones like diodes.

Takeaways

• 😀 Superposition is a property of linear systems used to analyze circuits with multiple sources.
• 😀 Superposition cannot be applied to circuits with nonlinear elements like diodes or solar cells.
• 😀 Superposition allows isolation of each voltage source's influence on the overall output of a circuit.
• 😀 To apply superposition, you ‘zero out’ all but one source at a time to analyze its effect.
• 😀 A zeroed-out voltage source behaves like a short circuit, while a zeroed-out current source acts as an open circuit.
• 😀 In a simple circuit with two voltage sources, superposition helps isolate the current contribution from each source independently.
• 😀 The example circuit involves a 3V source and a 6V source with resistors, where superposition helps break down the current into parts due to each source.
• 😀 With the 3V source active and the 6V source zeroed out, the current through a 2-ohm resistor can be calculated easily by dividing voltage by resistance.
• 😀 When the 3V source is zeroed out and the 6V source is active, the current through the circuit can also be calculated using the same principles.
• 😀 The total current in the circuit is the sum of the currents due to each source, demonstrating the effectiveness of the superposition method.
• 😀 Superposition only works for linear circuits, meaning that if any elements are nonlinear (e.g., diodes), the method cannot be applied.

Q & A

What is superposition in the context of electrical circuits?

Superposition is a method used in linear circuits to isolate the effect of each independent voltage or current source on the overall output. It allows us to analyze the contribution of each source separately and then combine them to find the total effect.

Can superposition be applied to circuits with nonlinear elements?

No, superposition can only be applied to linear circuits. Nonlinear elements like diodes, solar cells, or any component with a non-linear I-V characteristic cannot be analyzed using this method.

What kind of circuits can superposition be applied to?

Superposition can only be applied to circuits that contain linear elements such as resistors and voltage/current sources. These elements have a linear relationship between current and voltage.

How does superposition help when analyzing circuits with multiple sources?

Superposition allows us to isolate the influence of each source individually. By 'zeroing out' other sources and calculating the effects of each one, we can then sum these effects to determine the total current or voltage in the circuit.

What does 'zeroing out' a source mean in superposition?

'Zeroing out' a source means replacing it with its equivalent that has no effect on the circuit. For a voltage source, this means short-circuiting it (replacing it with a wire). For a current source, it means open-circuiting it (removing it from the circuit).

In the example, how do you calculate the current due to the 3V source?

To calculate the current due to the 3V source, we zero out the 6V source and simplify the circuit. The two 2-ohm resistors are in parallel, giving a combined resistance of 1 ohm. With a 3V source and 1 ohm total resistance, the current through the path is 3V / 3Ω = 1A, and then the current through each 2-ohm resistor is ½ A.

How is the current due to the 6V source calculated in the example?

To find the current due to the 6V source, we zero out the 3V source. The two 2-ohm resistors are in parallel, and the total resistance in the path is 3 ohms. The current through this path is 6V / 3Ω = 2A. Since the resistors are identical, the current divides equally, with each branch carrying 1A, but the directions of current flow in each branch are opposite, so the total current through the middle resistor is -1A.

What does the result of combining the currents from both sources tell us?

The total current through the 2-ohm resistor is the sum of the currents due to both the 3V and 6V sources. In the example, 0.5A from the 3V source and -1A from the 6V source combine to give a net current of -0.5A through the resistor.

What makes superposition a useful method for circuit analysis?

Superposition is useful because it simplifies the analysis of complex circuits with multiple sources. It allows engineers to calculate the individual effects of each source separately and then combine them, making it easier to understand the behavior of the circuit.

Why can’t superposition be used when dealing with nonlinear components in a circuit?

Nonlinear components, such as diodes or solar cells, do not follow a linear relationship between current and voltage. Superposition relies on the principle of linearity, which means the effects of different sources can be added together in linear circuits. Nonlinear components do not satisfy this condition, so superposition cannot be applied.