# Maximum Power Transfer Theorem: Calculation and Efficiency

The maximum power transfer theorem is a fundamental concept in electrical engineering that states that the maximum power is transferred from a source to a load when the impedance of the load is equal to the impedance of the source. In this article, we will explain the calculation of the maximum power transfer theorem and discuss its efficiency.

## Calculation of Maximum Power Transfer Theorem

To calculate the maximum power transfer theorem, we need to consider a circuit with a source and a load. The circuit can be represented by an equivalent circuit with a single impedance Z, which is the sum of the source impedance Zs and the load impedance ZL.

Z = Zs + ZL

The power transferred from the source to the load is given by the formula:

P = V^2 / Z

where P is the power, V is the voltage across the load, and Z is the impedance of the circuit.

To find the maximum power transferred from the source to the load, we need to differentiate the power equation with respect to Z and set it to zero.

dP / dZ = -V^2 / Z^2 = 0

Solving for Z, we get:

Z = Zs = ZL

This means that the maximum power is transferred from the source to the load when the load impedance is equal to the source impedance.

## Efficiency of Maximum Power Transfer Theorem

The efficiency of the maximum power transfer theorem is defined as the ratio of the power delivered to the load to the power supplied by the source. The efficiency is given by the formula:

where η is the efficiency, Pload is the power delivered to the load, and Psource is the power supplied by the source.

Using the formula for power, we can express the efficiency in terms of the voltage and current:

η = (Vload^2 / ZL) / (Vsource^2 / Zs)

where Vload is the voltage across the load, Vsource is the voltage supplied by the source, and Zs and ZL are the source and load impedances, respectively.

Substituting Z = Zs = ZL, we get:

η = 50%

This means that the maximum efficiency of the maximum power transfer theorem is 50%. In other words, only half of the power supplied by the source is delivered to the load.

## Conclusion

The maximum power transfer theorem is a fundamental concept in electrical engineering that states that the maximum power is transferred from a source to a load when the impedance of the load is equal to the impedance of the source. The calculation of the maximum power transfer theorem involves finding the load impedance that maximizes the power transferred from the source to the load. The efficiency of the maximum power transfer theorem is defined as the ratio of the power delivered to the load to the power supplied by the source. The maximum efficiency of the maximum power transfer theorem is 50%, which means that only half of the power supplied by the source is delivered to the load.