# Resistance doesn't depend on current

• Karol
In summary, the resistivity of metals is a constant and the resistance is fixed and does not depend on the current. However, when inserting the equation for resistivity into the equation for resistance, there appears to be a dependence. This is because while there are variables for resistance and current in the equation, the resistance itself cannot be changed by adjusting the current. Instead, the voltage changes. Just like how a car's speed is a constant factor between distance and time, resistance is a constant factor between electric field and current. So, while E and i may vary, the ratio between them, as represented by R, remains constant.
Karol

## 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

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

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.

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

The statement that resistance does not depend on current is not entirely accurate. While in some cases, such as in metals, the resistivity may be constant and thus the resistance is also constant, there are other materials where the resistance does depend on the current. This is because the resistivity of a material can change with temperature, pressure, or other external factors. In these cases, the resistance will also change with the current.

Additionally, the equation for resistance that you have provided only applies to materials with a constant resistivity. In cases where the resistivity is not constant, the equation becomes more complex and may include a dependence on current. Therefore, while the resistivity may be constant, the resistance itself can still vary with the current in certain situations.

## 1. What is resistance and how does it relate to current?

Resistance is the measure of a material's opposition to the flow of electric current. It is a property of the material and is typically measured in ohms (Ω). Resistance and current have an inverse relationship, meaning that as resistance increases, current decreases, and vice versa.

## 2. Why doesn't resistance depend on current?

Resistance is a characteristic of the material itself and is not affected by the amount of current flowing through it. This is because resistance is determined by the material's physical properties such as length, cross-sectional area, and temperature, which remain constant regardless of the current passing through it.

## 3. Can resistance change even if the current remains constant?

Yes, resistance can change if the material's physical properties change. For example, if the length of a wire is increased, its resistance will also increase, even if the current remains the same.

## 4. Is resistance the same for all materials?

No, resistance varies depending on the material. Materials with a higher number of free electrons, such as metals, have lower resistance compared to materials with fewer free electrons, such as insulators. This is due to the higher ease of electron flow in conductors compared to insulators.

## 5. How does temperature affect resistance?

Generally, as the temperature of a material increases, its resistance increases as well. This is because an increase in temperature causes the atoms in the material to vibrate more, making it more difficult for electrons to move through the material, thus increasing its resistance.

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