# finding the maximum power delivered from a baterry

by pentazoid
Tags: baterry, delivered, maximum, power
 P: 185 1. The problem statement, all variables and given/known data A battery of emf [insert symbol for emf here] and internal resistance is hooked up to a variable "load" resistance R. If you want to deliever the maximum possible power to the load, what resistance should you choose?(You can't change the emf and r, of course). 2. Relevant equations P=I^2*R=V^2/R Possibly V=[insert symbol for emf here]-Ir 3. The attempt at a solution I think what I should do is differentiate the Power with respect to the variable load R and sint dP/dR =0 P=V^2/R=([insert symbol for emf here]-Ir)^2/R
HW Helper
Thanks
P: 26,167
Hi pentazoid!

(what's "sint"? )
 Quote by pentazoid I think what I should do is differentiate the Power with respect to the variable load R and sint dP/dR =0 P=V^2/R=([insert symbol for emf here]-Ir)^2/R
Looks good!
P: 185
[QUOTE=tiny-tim;2038446]Hi pentazoid!

(what's "sint"? )

sorry , I meant to say since. [quote]
 Looks good!
seriously?

HW Helper
P: 2,886

## finding the maximum power delivered from a baterry

 Quote by pentazoid 1. The problem statement, all variables and given/known data A battery of emf [insert symbol for emf here] and internal resistance is hooked up to a variable "load" resistance R. If you want to deliever the maximum possible power to the load, what resistance should you choose?(You can't change the emf and r, of course). 2. Relevant equations P=I^2*R=V^2/R Possibly V=[insert symbol for emf here]-Ir 3. The attempt at a solution I think what I should do is differentiate the Power with respect to the variable load R and sint dP/dR =0 P=V^2/R=([insert symbol for emf here]-Ir)^2/R
This is correct but the current I depends on R as well so this not yet in a useful form.

I think it's simpler to use $$P = R I^2$$ with $$I = {\cal E} /(R+r)$$. Now differentiate wrt R, set to zero and solve for R.
P: 69
 Quote by nrqed This is correct but the current I depends on R as well so this not yet in a useful form. I think it's simpler to use $$P = R I^2$$ with $$I = {\cal E} /(R+r)$$. Now differentiate wrt R, set to zero and solve for R.
I'm trying to solve this problem but I'm having a hard time figuring out why I = (emf)/(r+R). Isn't V = emf when the conductivity is infinite? How is it infinite (or very big) in this case if the resistance is r.
Emeritus