Application of Maximum Power Transfer

What is maximum power transfer?

In DC circuits this theorem state that the source can transfer maximum power when the total resistance viewed from the load is equal to the value of the resistance of that load.

 Applications of Maximum Power Transfer

1. In communication system, maximum power transfer is always sought. For example in public address system, the circuit is adjusted for maximum power transfer by making load resistance (speaker) equal to the source resistance (amplifier). When source and load have the same resistance, they are said to be matched.
2. In car engines, the power delivered to the starter motor of the car will depend upon the effective resistance of the motor and the internal resistance of the battery. If the two resistances are equal, maximum power will be transferred to the motor to turn to the engine. 

 Proof of Maximum Power Transfer

At this point the simple circuit is can be a resemblance of a Thevinin's Circuit diagram where the internal resistance Ri similar to the Thevenin's resistance Rth while the supply voltage E in this circuit is similar to the open circuit voltage looking across the load RL.

Therefore in this case we can analyze the above diagram by means of a simple circuit analysis, thus....

 Maximized the resulting equation:

Mathematically it is proven that at this point we say that the internal resistance (Rth) is equal to the load resistance (RL) .

Sample Problem:

In the given circuit find the following:

1. The value of the load resistance RL to have maximum power transfer.

  Solution:

Solve for the Rth and RL:

1. To have maximum power it is required that Rth = RL. Therefore the load resistance RL= 73.3 ohms