Power supplied by a cell to a resistance R is given by P = [E/(R + r)]^2 * R. E and r, remain constant. For what value of R, maximum power is supplied to resistance R?

Ans: R=r

Can anyone explain the method?

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- Jun 29th 2008, 07:04 AMfardeen_genApplication of calculus?
Power supplied by a cell to a resistance R is given by P = [E/(R + r)]^2 * R. E and r, remain constant. For what value of R, maximum power is supplied to resistance R?

Ans: R=r

Can anyone explain the method? - Jun 29th 2008, 07:10 AMgalactus
If you differentiate, you get:

$\displaystyle \frac{E^{2}(r-R)}{(R+r)^{3}}$

Setting to 0 and solving we see that:

$\displaystyle (r-R)=0, \;\ \therefore{R=r}$