Power transfer and impedence matching.

[duckandcover]

What is the physical explanation for the power transfer in a circuit being maximum when the resistance of the system is equal to the internal resistance?

maybe heat loss?

any help would be appreciated as i understand the mathematical proof but do not know much about the physical causes.

 

[Mapes]

If the resistance of the load $R_\mathrm{load}$ is very low (so that the current I is approximately constant through the load and independent of $R_\mathrm{load}$), then the power transfer $I^2R_\mathrm{load}$ will be small. If the resistance of the load is very high (so that the voltage V is approximately constant across the load and independent of $R_\mathrm{load}$), then the power transfer $V^2/R_\mathrm{load}$ will be small. In between these two extremes is a happy medium, specifically at $R_\mathrm{load}=R_\mathrm{source}$.