# Resistance doesn't depend on current

1. Dec 18, 2014

### Karol

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Resistivity is field E divided by current to area: $\rho=\frac{E}{i/A}$
Resistance: $R=\frac{\rho L}{A}$

3. The attempt at a solution
$$R=\frac{\rho L}{A}=\frac{E\cdot L}{i}$$

2. Dec 18, 2014

### Staff: 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.

3. Dec 18, 2014

### rude man

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.

4. Dec 18, 2014

Thanks