Question

In which parameter superposition theorem is not applicable?

Answer 1

The superposition theorem isn't applicable in circuits where non-linearity is present. For instance, if a circuit element exhibits nonlinear characteristics—such as a diode or transistor operating outside its linear region—the superposition theorem, which relies on the principle that each independent source can be analyzed separately and then combined, will not yield accurate results. Nonlinear components create interactions between different sources that can't be analyzed independently.

Answer 2

The Superposition Theorem is a fundamental principle in linear circuit theory that states that in a linear circuit with multiple independent sources (voltage or current sources), the response (voltage or current) in any element of the circuit can be determined by summing the responses due to each source acting alone, with all other independent sources replaced by their internal resistances (usually zero for ideal voltage sources and infinite for ideal current sources).

However, the Superposition Theorem is not applicable under the following conditions:

1. **Nonlinear Circuits**: The Superposition Theorem is valid only for linear circuits. A circuit is linear if it follows the principle of superposition, meaning that its components obey Ohm's Law, and the circuit behavior can be described by linear differential equations. Nonlinear components, such as diodes, transistors, and other elements where the relationship between voltage and current is not linear, violate these conditions. In circuits containing such nonlinear elements, the principle of superposition cannot be used directly because the response of the circuit cannot be simply added up from individual responses.

2. **Time-Varying Components**: Superposition is typically applied to circuits with time-invariant components. If the circuit elements or the sources are time-dependent, the theorem might not hold. For instance, if you have sources or elements whose properties change with time (e.g., a resistor whose resistance changes with temperature or a source whose frequency changes over time), then the principle of superposition may not be applicable.

3. **Nonlinear Sources**: In circuits where the sources themselves are nonlinear (for instance, if you have a source whose voltage depends on the current through it in a nonlinear way), the superposition principle does not apply. This is because the response of the circuit depends on the nonlinear interaction between the sources and the circuit components, which cannot be separated and analyzed individually.

4. **Non-Superposable Effects**: There might be specific cases in practical circuits where the effects of different sources are not simply additive due to interaction between them. For example, in circuits involving strong magnetic or electric field interactions (like in transformers or circuits with high-frequency components), the assumption of linear superposition might not hold.

In summary, the Superposition Theorem is not applicable to nonlinear circuits, circuits with time-varying components, nonlinear sources, and situations where superposable effects do not hold.