Energy Dissipation Across a Resistor

[boredbluejay]

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: P_R=i²R
Voltage is the same for resistors in parallel
1/R_total=1/R+1/R₀
i_total=V/R_total

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!

 

[tiny-tim]

hi boredbluejay!

isn't resistance proportional to length?

 

[boredbluejay]

I guess, but by what factor. >< I'm sorry, I'm really bad at this.

 

[lewando]

You have two points on the x,R plane: (0,0) and (10,R₀). With this, determine the linear relationship R = mx + b.