# Resistance doesn't depend on current

## Homework Statement

In metals the resistivity ρ is constant and the resistance R is fixed and doesn't depend on the current, but when i insert the equation of ρ into R i do get a dependence.

## Homework Equations

Resistivity is field E divided by current to area: ##\rho=\frac{E}{i/A}##
Resistance: ##R=\frac{\rho L}{A}##

## The Attempt at a Solution

$$R=\frac{\rho L}{A}=\frac{E\cdot L}{i}$$

mfb
Mentor
E*L=V, so you get the usual equation R=V/I. While there are R and I in the equation, this is not considered as "resistance depends on current" - you cannot change resistance by changing current, you will change the voltage instead. Voltage and current are proportional to each other, and the factor between them is the constant (just material-dependent) resistance.

A similar example: Imagine a car driving at a constant speed v. With time t and distance d, we can set up the equation v=d/t. Does the speed depend on time now? No - speed is the constant factor between distance and time.

rude man
Homework Helper
Gold Member
E and i are related by a constant: E = (ρ/A)i. So E/i is a constant.
So R = ρL/A is also a constant.

Thanks