# Are values of resistivity independent of the cross-section and length of the resistor?

I was reading resistivity values for different materials on the wikipedia page. They report the values for standard temperature, but they give no information about the cross-section or length of the material/resistor. Are this values independent of the cross-section or the length of the resistor?

• A resistor as a component has different geometries, so the size of the component itself typically does not affect resistance (i.e. you can even have a resistor laser trimmed and it won't change physical size, but the conductor on it will have a smaller cross section at a point). The length and cross-section of a conductor do affect resistance. – Wesley Lee Nov 28 '17 at 18:03
• You need to fit the numbers from that table into the formulas at the top of the article that does include length and area. – Trevor_G Nov 28 '17 at 18:04
• If you are talking about component resistors, the size of the package is only really pertinent to heat dissipation. What is inside the individual resistor packages is different sizes and materials.. – Trevor_G Nov 28 '17 at 18:09
• @Trevor - I might have gotten a term wrong? A longer or thinner conductor has higher resistance. – Wesley Lee Nov 28 '17 at 18:10
• hmm, I assumed OP was confusing resistance with resistivity and forgot to explicitly mention it... Since resistor and resistivity were mentioned, but not resistance. – Wesley Lee Nov 28 '17 at 18:13

Resistivity is a property of a material. Resistance is a property of an item that is made up of a material.

All copper wires, irrespective of their shape and size, have approximately the same resistivity, but a long, thin copper wire has a much larger resistance than a thick, short copper wire. https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

The basic formula for resistance of an object is as follows:

$$R=\frac{\rho\ l}{A}$$

• $R$ is resistance
• $\rho$ is the resistivivity of the material
• $l$ is the length of the object
• $A$ is the cross-sectional area of the object

The resistivity of annealed copper per ASTM B3 is 0.15328 Ω·g/m² at 20°C. This works out to a resistance of 0.15328 Ω for a wire of length 1 m and mass 1 g (diameter 378.45 µm). A wire of the same diameter of length 2 m will have a resistance of 0.30656 Ω.

• On the wikipedia page are reported some value for resistivity not resistance. I don't understand how this value are calculated. Maybe I sould edit the question in this sense – Gabriele Scarlatti Nov 28 '17 at 18:25
• @GabrieleScarlatti in the equation $R = \rho \frac{l}{A},$ resistivity is material property but all other terms are measured. Hence it is calculated from this formula itself knowing all other parameters already, for various lengths or size, different readings are obtained but when back calculated the resistivity remains roughly constant. – rsg1710 Nov 28 '17 at 18:33
• Ah ok so we have that even if we change L and A, but we mantain the same I and the same V ( and so the same R), the resistivity does not change. is that right? – Gabriele Scarlatti Nov 28 '17 at 18:36
• @GabrieleScarlatti yes if we change L and A by same values therefore not changing Resistance. If at all L and A are changed differently then you would get different values of V and I (hence different R) but the value of resistivity when back calculated comes out to be same as before. – rsg1710 Nov 28 '17 at 18:39
• @rsg1710 Thabk you very much! – Gabriele Scarlatti Nov 28 '17 at 18:53

Let's start with a cube of material (exact size not important for now), with two opposing faces coated with a conductive material of zero resistance. You with me? Now you can apply a voltage across the two electrode faces, measure the current, and derive the resistance using Ohm's Law.

Now stack 4 of theses cubes together face-to-face, making a block 4 units long. The resistance is clearly 4 times the resistance of 1 cube. In other words, the resistance will be proportional to the length of the assembly.

Now try connecting 4 of these in parallel. The resistance will be 1/4 of a single cube. So the resistance is inversely proportional to the area of the assembly.

This says that, using a unit cube as a starting point, and calling its resistance a reference point, the resistance of any block of the material can be expressed as the resistance of a unit cube multiplied by the length and divided by the area (assuming the block as a rectangular prism).

This in turn says that we can talk about the resistance of a unit cube as being a material-dependent quality (which we call resistivity) multiplied by unit length and divided by unit area, which means that the resistivity will have the units of ohms times length - you can do the math to see how the units cancel. Since you can do this for a unit cube, then scale that to any desired size, you can use that resistivity for any size conductor.