SOLUTION: 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 dissipate

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

RELATED QUESTIONS
Ohm's law states that V=IR for a simple circuit, where V is the total voltage, I is the... (answered by ikleyn)

A constant voltage is applied to a circuit that has a variable resistor. The current... (answered by stanbon)

In electronics, according to Ohm's law, E = IR, where "E" is voltage (measured in... (answered by Alan3354)

the voltage in a circuit is given by the equation V= square root of PR, where P is the... (answered by bucky)

the voltage in a circuit is given by the equation V = square root of PR, where P is the... (answered by ankor@dixie-net.com)

Complex numbers are used in electronics to describe the current in an electric circuit.... (answered by ankor@dixie-net.com)

If P is power (in watts) and R is resistance (in ohms), then the voltage V necessary to... (answered by stanbon)

Ohm's law states the formula E= IR in which E is the voltage of the circuit measured in... (answered by )