According to maximum power transfer theorem, when is the maximum power absorbed by onenetwork from another network ?a)The impedance of one of the network is half that of the otherb)The impedance of one is the complex conjugate of the otherc)The impedance of one is equal to that of the otherd)Only the resistive parts of both are equalCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

According to the maximum power transfer theorem, the maximum power is absorbed by one network from another network when the impedance of one network is the complex conjugate of the other.

Here's a detailed explanation:

Explanation:
1. Maximum Power Transfer Theorem:
The maximum power transfer theorem states that maximum power is transferred from one network to another network when the impedance of the load is the complex conjugate of the source impedance. In other words, the load impedance should be equal in magnitude but opposite in sign to the source impedance.

2. Impedance of one network is the complex conjugate of the other:
When the impedance of one network is the complex conjugate of the other, it implies that the real parts of the impedance are equal, while the imaginary parts are equal in magnitude but opposite in sign. This condition satisfies the maximum power transfer theorem.

3. Understanding Impedance:
Impedance is a complex quantity that represents the opposition to the flow of alternating current (AC) in a circuit. It consists of both resistance (real part) and reactance (imaginary part). The impedance is typically represented as Z = R + jX, where R is the resistance and X is the reactance.

4. Power Transfer in AC Circuits:
In AC circuits, the power transfer is maximum when the load impedance matches the complex conjugate of the source impedance. This condition ensures that the load absorbs the maximum amount of power from the source.

5. Complex Conjugate Impedance Matching:
When the impedance of the load is the complex conjugate of the source impedance, the reactive components cancel each other out, leaving only the resistive components. This minimizes the reactive losses in the circuit and maximizes the power transfer.

6. Other Options:
The other options mentioned in the question (a, c, and d) do not satisfy the conditions of the maximum power transfer theorem. In option a, the impedance ratio is not balanced, which leads to power loss. In option c, equal impedance alone does not guarantee maximum power transfer. Option d only considers the resistive parts, ignoring the reactive components, which is not correct.

In conclusion, the correct option is B - when the impedance of one network is the complex conjugate of the other. This condition ensures maximum power transfer between the networks by minimizing reactive losses and maximizing power absorption.

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