Maximum Power Transfer Theorem

Suppose we have a voltage source orbattery that's internal resistance is Riand a load resistance RL is connected across this battery . Maximum power transfer theorem determines the value of resistance RL for which, the maximum power will be transferred from source to it. Actually the maximum power, drawn from the source, depends upon the value of the load resistance. There may be some confusion let us clear it.

Power delivered to the load resistance,

To find the maximum power, differentiate the above expression with respect to resistance RLand equate it to zero. Thus,

Thus in this case, the maximum power will be transferred to the load when load resistanceis just equal to internal resistance of the battery .
Maximum power transfer theorem can be applicable in complex network as follows-

A resistive load in a resistive network will abstract maximum power when the load resistanceis equal to the resistance viewed by the load as it looks back to the network. Actually this is nothing but the resistance presented to the output terminals of the network. This is actuallyThevenin equivalent resistance as we explained in Thevenin's theorem if we consider the whole network as a voltage source. Similarly, if we consider the network as current source, this resistance will be Norton equivalent resistance as we explained in Norton theorem.