Question

What is the efficiency of the maximum power transfer theorem?

Answer 1

The efficiency of the Maximum Power Transfer Theorem (MPTT) refers to how effectively power is transferred from a source to a load when the maximum power is delivered.

The Maximum Power Transfer Theorem states that maximum power is transferred to the load when the load resistance (R_L) is equal to the source resistance (R_S). This means that the condition for maximum power transfer is \( R_L = R_S \).

Efficiency of Maximum Power Transfer

However, the efficiency of power transfer is not very high at this point because half of the power from the source is dissipated in the source resistance, and the other half is delivered to the load.

The efficiency (\( \eta \)) can be calculated using the formula:

\[
\eta = \frac{\text{Power delivered to the load}}{\text{Total power supplied by the source}} \times 100
\]

Given that P_max (power delivered to the load) is half of the total power supplied by the source, the efficiency at maximum power transfer is:

\[
\eta = \frac{P_{load}}{P_{total}} \times 100 = \frac{\frac{P_{source}}{2}}{P_{source}} \times 100 = 50\%
\]

Conclusion:

At the point of maximum power transfer (where \( R_L = R_S \)), the efficiency is 50%. This means that half of the power generated by the source is used to power the load, and the other half is lost as heat in the source resistance.