Thread: application 3

A direct current generator has an electromotive force of E volts and an internal reistance of r ohms. E and r are constants. If R ohms is the external resistance, the total resistance is (r + R) ohms and if P watts is the power then
[html]
E²R
P = ----------
(r + R)²
[/html]
What external resistance will consume the most power?

Originally Posted by cazimi

A direct current generator has an electromotive force of E volts and an internal reistance of r ohms. E and r are constants. If R ohms is the external resistance, the total resistance is (r + R) ohms and if P watts is the power then
[html]
E²R
P = ----------
(r + R)²
[/html]
What external resistance will consume the most power?

You want to solve:

dP/dR = 0,

well:

dP/dR = E^2/(r+R)^2 -2 E^2 R/(r+R)^3 = 0

which may be rearranged (as E != 0) to:

2R/(r+R) = 1,

or R=r.

RonL