Question

If a resistance of R ohms is connected across a battery of E volts with internal resistance (the resistance within the battery) r ohms, then the power in watts dissipated in the external resistor is given by P = (E^2R)/((R+r)^2. If E and r are fixed, find R so that the power dissipated externally is a maximum.

Answer 1

Physics 2?

Answer 2

Calculus 1

Answer 3

Interesting*

Answer 4

I found an answer but I do not know if it is right.

Answer 5

\[R = \frac{ 1 }{ 2 }E ^{2} - \frac{ 1 }{ 2 }r - \frac{ 1 }{ 2 }\sqrt{E ^{4}-6rE ^{2}+r ^{2}}\]

Answer 6

@jim_thompson5910 @jdoe0001

Answer 7

@Zarkon @zepdrix

Answer 8

@TheSmartOne

Answer 9

@geerky42