# Help compare my results to the maximum power transfer theorem and explain using algorithms

So below is an image of the relationship between efficiency of a circuit and the resistance of the load, as you can see the maximum efficiency occurs when the two resistances are equal. here is a graph of my recorded data, it is clear that it follows that above model, however it is graphing the ability of varying wires to heat water. That is, it is essentially graphing the ability of the wire to transfer energy to the water. Why do my results follow this path? also how can I explain using theory and maths that there is a maximum power and beyond that when you increase the resistance power drops?

• Please show the equipment setup and explain the procedure you used to get the data for your plot. Aug 20 '14 at 9:22
• For an intuitive proof consider a very small RL: Current will be maximum but very little voltage across it so very little power in the load. Now consider very large RL: Voltage is maximum but little current so again very little power. We must therefore have a choice of RL for maximum power. For a rigorous mathematical proof see Andy's answer. It's what I would have posted if he had not beet me to it. Aug 20 '14 at 12:13 