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The Maximum Power Output of a Potential Divider

A potential divider (shown below) divides a supply voltage between two resistors in the the ratio of their resistances so that the larger resistance gets the larger share of the voltage.

The power supplied by the circuit is given bywhereis the output voltage andis the current, the supply voltage divided by the toral resistanceso that

We differentiate this with respect toto find the maximum output power.

Then