Finding the maximum power delivered from a baterry

[pentazoid]

Homework Statement

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).

Homework Equations

P=I^2*R=V^2/R
Possibly V=[insert symbol for emf here]-Ir

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

 

[tiny-tim]

Hi pentazoid!

(what's "sint"? )

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!

 

[pentazoid]

Hi pentazoid!

(what's "sint"? )

sorry , I meant to say since.

Looks good!

seriously?

 

[nrqed]

Homework Statement

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).

Homework Equations

P=I^2*R=V^2/R
Possibly V=[insert symbol for emf here]-Ir

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.

 

[Marioqwe]

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.

 

[cepheid]

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?

To be honest, I don't know what you're talking about.

Kirchoff's voltage law (KVL) says that the sum of the voltages around a closed loop in a circuit has to equal zero (this is just the conservation of energy, when you think about it). In other words, the voltage drop across the two resistors has to be equal to the voltage across the battery terminals (which is just the emf). Everything is in series, so current through the circuit is the total voltage over the total resistance, hence I = ε/(r+R).