Calculate the resistance of a copper wire of 1-cm length, 1 -mm radius, and 1.72 ×10^-8 Ω-m resi

Calculate the resistance of a copper wire of 1-cm length, 1...

Key Concepts

Electrical Resistance

Electrical resistance quantifies the opposition a material presents to the flow of electric current. It is influenced by both the material's intrinsic properties and its geometric dimensions, and is measured in ohms (?).

Resistivity

Resistivity is a fundamental property of a material that describes how strongly it resists current flow. It is independent of the object's shape and size and is typically measured in ohm-meters (?·m). Lower resistivity indicates better conductivity.

Resistance Formula for Uniform Conductors

For a uniform conductor, the resistance (R) can be calculated using the formula R = ?(L/A), where ? is the resistivity, L is the length of the conductor, and A is its cross-sectional area. This formula directly relates the material properties and the physical dimensions to the overall resistance.

Cross-Sectional Area Calculation

The cross-sectional area of a conductor, especially when it has a circular shape, plays a crucial role in determining the resistance. It is calculated using the formula A = ?r², where r is the radius of the conductor. A larger area allows more charge to flow through, reducing resistance.

Transcript

00:01 23 .38, so we want to calculate the resistance of a piece of copper wire.

00:07 It has a length l of one centimeter, a radius r of one millimeter, and a resistivity, which is usually denoted by the greek letter row.

00:16 This is a lowercase row.

00:19 1 .72 times 10 to the negative 8 oom meters.

00:26 And this is just a constant for a given material that lets you calculate the resistance of a given piece of it that has you know, a size and shape that you know.

00:41 So let's imagine this is our piece of wire.

01:02 L -wong and has a radius of r.

01:05 Now, i actually, i'm not sure.

01:10 It doesn't appear to me that the equation for this is actually given anywhere in the chapter.

01:15 I might have missed it, but we can actually figure out what it should be, or at least understand why what it is should be what it is based on what it tells us.

01:31 So if you have a piece of material that has some cross -sectional shape that's the same throughout its length, and then it has some length.

01:43 So basically, i mean, this could be a, this could have a square cross -section, or it could be some sort of oval, or it could have a a star shaped cross -section doesn't really matter the resistance is going to be the resistivity and thinking about the units we have here this makes sense we'll get umms and then we need to multiply this by something that ends up having units of one over meters so we know that the longer our material is the higher the resistance will be this is sort of like having a longer thin pipe will you know create more resistance to the flow of water and then we also know that the the wider or thicker the the conductor is is sort of analogous to having a pipe that has well that's that's also wider and we can express that in a way that doesn't depend on what the shape is by just putting saying this is the area and so if we look at this we have om meters times meters divided by meters squared.

03:29 So one meter cancels out from from here and then the other one cancels out from here.

03:36 So we have oms.

03:37 So this works out in terms of giving us the correct units.

03:41 And it turns out that there's not any weird factors of two or pi or something in here that that we need...

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