- #1
millifarads
- 5
- 0
Homework Statement
The question asks for resistance R of a disk with radius r and fixed width w, whose cross sectional area is variable. Unlike in the picture below, the resistor is not connected to the circuit on the flat ends, but on the cylindrical sides.
Homework Equations
The Attempt at a Solution
With [tex]R = \rho \frac{L}{A}[/tex]L = 2r, ρ is given, but I'm having trouble setting up an expression for the cross sectional area. Normally, for cross sectional area of this type of problem it's just the area of a circle, and some integration will be required with the bounds being the radius at each end.
But here my initial thought is to set up an expression for a one dimensional line along the top of the disk, then multiple that by the width of the disk, w. The area will change with the radius though, so I'm not sure if integration is required.
From the equation for the circle of radius r, I get
[tex]y = \sqrt{r^2-x^2}[/tex]
which then needs to be multiplied by 2, and then by w to get a sort of cross sectional area:
[tex]R = \rho \frac{2r}{2w*\sqrt{r^2-x^2}}[/tex]
Am I on the right track?