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ohgeecsea
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Homework Statement
(a) In the figure shown, show that the rate at which energy is dissipated in R as thermal energy is a maximum when R = r. (b) Show that this maximum power is P = EMF2/4r.
http://www.practicalphysics.org/imageLibrary/jpeg400/208.jpg [Broken]
The only difference between this picture and the one in my book is that they specify the direction of current going one way (clockwise) throughout the whole circuit.
Homework Equations
P = i2r
EMF - ir - iR = 0
P = EMF2/4r
The Attempt at a Solution
(b) switching EMF - ir - iR = 0 so that it is equal to i:
i = EMF / (r + R)
and assuming r = R:
i = EMF / 2r
substituting this in for i in P = i2r, you get:
P = [ EMF / 2r ]2r
P = EMF2r/4r2
P = EMF2/4r
(a) for r = R, as shown above:
P = EMF2/4r
and for r =/= R:
P = EMF2r/(r2 + 2rR + R2)
Thing is, I don't really understand how the rate of dissipation of thermal energy is greatest at r = R. Isn't this just a linear relationship? Wouldn't the power be greatest if the internal resistance was zero, as in an ideal battery?
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