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?