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Finding the maximum power delivered from a baterry 
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#1
Jan1709, 11:33 AM

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 


#2
Jan1709, 01:06 PM

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Hi pentazoid!
(what's "sint"? ) 


#3
Jan1709, 06:15 PM

P: 185

[QUOTE=tinytim;2038446]Hi pentazoid!
(what's "sint"? ) sorry , I meant to say since. [quote] 


#4
Jan1709, 11:36 PM

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Finding the maximum power delivered from a baterry
I think it's simpler to use [tex] P = R I^2 [/tex] with [tex] I = {\cal E} /(R+r) [/tex]. Now differentiate wrt R, set to zero and solve for R. 


#5
Nov1511, 10:44 PM

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#6
Nov1511, 11:31 PM

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PF Gold
P: 5,197

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). 


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