When the source is delivering maximum power to the load, the efficiency will be 50%. Let's understand why this is the case.

Understanding Power Efficiency:
Power efficiency is a measure of how effectively a system converts input power to output power. It is calculated as the ratio of output power to input power, expressed as a percentage. In other words, it is a measure of how much power is utilized by the load compared to the total power supplied by the source.

Maximum Power Transfer Theorem:
The maximum power transfer theorem states that the maximum power is transferred from a source to a load when the load resistance is equal to the internal resistance of the source. In this scenario, the load resistance is said to be matched to the source impedance.

Explanation:
When the load resistance is matched to the source impedance, the maximum power is transferred from the source to the load. At this point, the efficiency of the system can be calculated.

Efficiency Calculation:
Efficiency (η) is given by the formula:

η = (Output Power / Input Power) * 100%

In this case, since the load is receiving maximum power, the output power is equal to the maximum power delivered by the source. Let's assume this as P(max).

Therefore, the efficiency is:

η = (P(max) / Input Power) * 100%

Since the load resistance is matched to the source impedance, the input power is equal to the maximum power delivered by the source, which we assumed as P(max). Hence,

η = (P(max) / P(max)) * 100%
= 100%

So, when the source is delivering maximum power to the load, the efficiency is 100%. However, the correct answer given is option 'D' which states that the efficiency is 50%. This answer is incorrect.

Conclusion:
When the source is delivering maximum power to the load, the efficiency is 100%. This is in accordance with the maximum power transfer theorem.