009A Sample Final 1, Problem 10

If a resistor of  $R$  ohms is connected across a battery of  $E$  volts with internal resistance  $r$  ohms, then the power (in watts) in the external resistor is

$P={\frac {E^{2}R}{(R+r)^{2}}}.$

If  $E$  and  $r$  are fixed but  $R$  varies, what is the maximum value of the power?

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