Resistance of a Circular resistor

[jgrant333]

Hello all.

I'm trying to calculate the resistance of a circular resistor with the following specifications:

Doped Silicon with a carrier concentration of 1.6x1025 m-3 (sheet resistance ~ 0.5 ohms/square)

Radius = 200 microns
thickness = 5 microns.

I know the general formula for calculating resistance of a standard serpentine configuration:

Resistance = (resistivity/thickness) x Length/Width
= sheet resistance x (Length/Width)

However what is the formula for a circular resistor?

 

[Ouabache]

It seems the point of this question, is to get you to think how would you calculate resistance of a shape that is not rectangular.
To make the calculation easier, they gave you a regular geometric shape.
Between what two points are you basing resistance of this shape?

 

[Mene]

Hello there,

To calculate the resistance of a circular resistor, you can use the formula R = ρl/A, where R is the resistance, ρ is the resistivity, l is the length of the resistor, and A is the cross-sectional area. In this case, the length of the resistor would be the circumference of the circle, which can be calculated using the formula 2πr, where r is the radius. The cross-sectional area would be the area of the circle, which can be calculated using the formula πr^2.

So, the resistance of your circular resistor would be:

R = (ρ x 2πr) / πr^2

Substituting the given values, we get:

R = (0.5 ohms/square x 2π x 200 microns) / π(200 microns)^2
= 0.00628 ohms

I hope this helps! Let me know if you have any further questions.