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Question 1070502: A circuit consists of a battery with voltage E, constant internal resistance r, and a variable
external resistance R. When current flows through the circuit, the power P dissipated in the
external resistance is given by
P =
E^2R/
(R + r)^2
.
Assume that E, R and r are positive constants. Show the largest power dissipation occurs
when R = r. Identify the interval you are maximized over and show your solution
is the maximum.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! P = E^2R/(R+r)^2, with r = const
We need to maximize this expression with respect to R, so we need to solve dP/dR = 0
If you perform the differentiation, you should be left with dP/dR = V^2/(R+r)^2 -2V^2R/(R+r)^3 = 0
Multiply both sides by (R+r)^2/V^2:
1 - 2R/(R+r) = 0 -> R + r = 2R -> R = r
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