# Voltage drop in an infinite wire

• YaroslavVB
In summary, the conversation discusses the issue of finding voltage at intermediate points in a finite wire of known resistivity and an infinite wire of known resistance. The solution to this problem involves using Ohm's Law and the linear voltage drop between two points with known voltages. There is also a mention of the connection between random walks and heat flow, which can be explored further in a textbook on the subject.
YaroslavVB
Suppose I have finite wire of known resistivity. I know voltage is 0 volts at x=-1 and x=1, and 1 volt at x=0. How do I find voltage at intermediate points?

Last edited:
YaroslavVB said:
Suppose I have infinite wire of known resistance and inject current into position x=0. How do I find voltage distribution?

An infinite wire would have an infinite resistance. I think you mean a known resistivity, or resistance per unit length. If a current is induced in the wire, you just use Ohm's Law to calculate the voltage drop per unit length.

Yes, I probably mean resistivity, and know voltage instead of current, updated post with fixes

It's going to be 1V everywhere, and no current will flow, because the total resistance is still infinite.

OK, another update.

YaroslavVB said:
OK, another update.

It's better if you just post an updated question in each of your replies, instead of editing the original post. It's confusing if you keep changing the original question.

To try to answer your question, since the current must be the same everywhere in the wire, the linear voltage drop will be the same everywhere. So if you have two points with known voltages, the voltage will vay linearly between those two points.

Yup. So V(x) = (1 - |x|) Volts.

In general:

$$I = \sigma E(x)$$

For all x, where sigma is conductivity = 1/resistivity, and

$$V(a,b) = \int_a^b dx E(x)$$

(Did I miss a minus sign somewhere? I feel like I did...)

I was trying to see if limiting distribution of a a symmetric random walk on R can be modeled as voltage, but now it doesn't seem there's a direct connection

No. No connection. But random walks are related to heat flow. You might want to look at that.

What's a good textbook for that?

## 1. What is voltage drop in an infinite wire?

Voltage drop refers to the decrease in electrical potential along a wire or circuit due to the resistance of the material. In an infinite wire, this drop is constant and can be calculated using Ohm's Law (V=IR), where V is voltage, I is current, and R is resistance.

## 2. What causes voltage drop in an infinite wire?

Voltage drop is caused by the resistance of the material the wire is made of. In an infinite wire, the resistance is constant and can be affected by factors such as temperature, material composition, and length of the wire.

## 3. How is voltage drop measured in an infinite wire?

Voltage drop in an infinite wire can be measured using a voltmeter, which measures the potential difference between two points in the circuit. The voltage drop can also be calculated using Ohm's Law, as mentioned before.

## 4. What are the effects of voltage drop in an infinite wire?

Voltage drop can result in a decrease in the amount of usable voltage in a circuit, which can lead to reduced performance or malfunction of electrical devices. It can also cause overheating and damage to the wire itself.

## 5. How can voltage drop in an infinite wire be reduced?

To reduce voltage drop, the wire can be made with materials that have lower resistance, or the wire can be made thicker to decrease the resistance. Additionally, keeping the wire length as short as possible can also help reduce voltage drop.

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