Energy Dissipation Across a Resistor

AI Thread Summary
The discussion focuses on calculating the rate of energy dissipation across a resistor R as a function of the position x of a sliding contact. The relevant equations include the power dissipated (PR = i²R) and the relationship for total resistance in parallel circuits. Participants suggest expressing resistance R in terms of the position x and the total resistor R0, emphasizing that resistance is proportional to length. A linear relationship between resistance and position is proposed, using points on the x,R plane to find the slope. The conversation highlights the need for clarity on how to derive the function for energy dissipation based on the changing resistance.
boredbluejay
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Homework Statement


A battery is connected across a uniform resistor R0. A sliding contact can move across R0 from x=0 to x=10cm at the right. Moving the contact changes how much resistance R is to the left of the contact and how much is to the right. Find the rate at which energy is dissipated in R as a function of x.


Homework Equations


Energy dissipated: PR=i2R
Voltage is the same for resistors in parallel
1/Rtotal=1/R+1/R0
itotal=V/Rtotal


The Attempt at a Solution


I tried to express R in terms of x and R0, but I got stuck. I honestly have no idea how to begin, or even if all of the equations that I wrote above are relevant to this question. Could someone please give me a hint that'll point me in the right direction? Thanks!
 
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hi boredbluejay! :smile:

isn't resistance proportional to length? :wink:
 
I guess, but by what factor. >< I'm sorry, I'm really bad at this.
 
You have two points on the x,R plane: (0,0) and (10,R0). With this, determine the linear relationship R = mx + b.
 
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