Maximum Power Transfer Theorem

The Maximum Power Transfer Theorem states that the maximum power is delivered to a load when the resistance of the load is equal to the source resistance.

So what does that mean? It means that in order to deliver maximum power to a load of a circuit we should aim to match the resistance of our source which is driving the load to the load resistance. This is a very important point which should be kept in mind! Expressed mathematically, we need:


We can derive the above by considering the circuit below:

To determine the maximum power, we need an expression for power in terms of resistance and then we can differentiate and equate to zero and solve for R:

From here we can differentiate with respect to Rl using the chain rule and equate to zero to find the maximum:

If we define the denominator to be u, then the above becomes:

Taking the derivative with respect to u:

For the chain rule, we then need to take the derivative of u with respect to Rl:

From here we can apply the chain rule to determine the derivate with respect to Rl:

The maximum can then be calculated by equating this to 0:

Which is what we expect! Maximum power is transferred to the load when the source resistance matches the resistance of the load.


1. Calculate the value of Rs such that maximum power is delivered to the load in the following circuit:

Maximum power is delivered when Rs is equal to Rl i.e. when the source resistance is 10kΩ.

Ready for the next module? Return to the course home.