# Ressistance when current-density is not constant

• center o bass
In summary, the conversation discusses the effect of varying current density on the resistance of a wire with length L and cross-sectional area A(x). The speaker is struggling with understanding how resistance can be related to current density when electric field is not constant. The other person explains that resistance is defined as the potential drop divided by the current, and since the electric field can be calculated for differential elements, resistance can still be calculated even when it is not constant.
center o bass
I am trying to figure out how it would effect the ressistance R of a wire with length L and variyng cross-sectional area A(x) if the current density was a fuction of the radius of the wire. That is J = J(r).

I'm having trouble with this when it seems like ressistance is the result of a derivation of ohm's law assuming constant E-field such that $$E = \frac{J}{\sigma} = \frac{V}{l}$$, but if E is not constant how can one then relate the ressitance to the current-density J?

A qualitative answer is good enough.

But if E is not constant how can one then relate the resistance to the current-density J?
Resistance is by definition ΔV/i(and this is not Ohm's Law).Even though the electric field is not constant it is a law accurate for differential elements. So if you calculate E(x) function and integrate for the corresponding potential drop you can calculate resistance.

## 1. What is resistance when current-density is not constant?

Resistance is a measure of how much a material resists the flow of electric current. When the current-density is not constant, it means that the current is not evenly spread out throughout the material, resulting in varying levels of resistance.

## 2. How does resistance change when current-density is not constant?

When current-density is not constant, the resistance will also not be constant. As the current-density increases, the resistance will decrease and vice versa. This is because the more evenly the current is distributed, the easier it is for it to flow through the material, resulting in lower resistance.

## 3. What factors affect resistance when current-density is not constant?

The main factor that affects resistance when current-density is not constant is the material's conductivity. Materials with higher conductivity will have lower resistance, even when the current-density is not constant. Other factors that can affect resistance include temperature and the physical dimensions of the material.

## 4. How can we calculate resistance when current-density is not constant?

To calculate resistance when current-density is not constant, we can use Ohm's Law, which states that resistance is equal to voltage divided by current. However, since the current is not constant, we must use an average value for current and consider the varying current-density throughout the material in our calculations.

## 5. Why is it important to understand resistance when current-density is not constant?

Understanding resistance when current-density is not constant is important in many practical applications, such as in electrical circuits and power transmission. It allows us to predict and control the flow of electricity through different materials, and to design more efficient and reliable systems that can handle varying levels of current-density.

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