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Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).

$\frac{D_{\mathrm{Al}}}{D_{\mathrm{Cu}}}=1.24$

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

McMaster University

Lectures

11:53

In physics, a charge is a …

10:30

The electric force is a ph…

01:51

A copper wire and an alumi…

01:32

Aluminum and copper wires …

01:12

How must the diameters of …

04:23

Two wires have the same le…

02:59

What diameter must a coppe…

06:56

02:41

(II) Two aluminum wires ha…

03:13

03:30

A circuit calls for a $0.5…

03:22

Ratio reasoning Determine …

03:38

(a) What are the ratios of…

01:50

Nine copper wires of lengt…

02:27

Two wires $A$ and $B$ made…

02:51

(II) Calculate the ratio o…

02:15

A copper wire joins an alu…

03:31

00:49

(I) What is the resistance…

02:14

02:31

Wires 1 and 2 are made of …

01:02

In household wiring, coppe…

in this particular sum, it is given that aluminum and copper, while having the same distance for you nickel and dime. We need to find the ratio diameter off, leaving him to the copper wire. So we need to use the basic formula as our is equal to grow into upon a burial stands for their festivity. Instance for the length of the world and he's cross sectional area. Now that's why did this cross sectional area is concerned? It's formulas by R Squared, which is acquitted by into D by through the whole square which is spying to the square. Therefore now we'll put this value in the formula for our that is our into a festivity into l and upon by d squared. Very careful. So ultimately, what we get here is four times brother Stevie Deland on buy into damage a square. Now we need to convert this He dumps off down ago. So put it in the square EZ hold times rule into a upon by and are coming though you know better. So therefore, D stands for diameter is given us for for old time's ill a phone five times are race to one major that is squared off this. No, let's take the diameter for aluminum. It is the same formula that we're going to use. So that is four times rule off, leaving him multiplied by Excellent off the way upon by two. Oh, and this will be square. Similarly, if you want to take the damage off a copper, then it could be in dumps off four times the festivity of copper lent off the copper wire by drawing. We're taking the same notation for Lent as well as our because it has been given that they're having the same resistance but uniquely not be sickening. We need to get a show for it. Okay, so taking ratio. Let's see what we get now. Immigration. It would be damaging off living with this picture. Dime again of corporate four times, right? Stupid Your family Amenia indolent off the wire. Bye. I race too off at the same time. Then you might agree. We need to take the square. The result and really why? But we take the modification of the same return could be by our race to harm that is squared off fire four times. But it's still pretty off copper and its land. It's great to see you are committed these two terms. They get cancer DDE competing the same time if you consider four and it's lent with the specter aluminium four times lance with copper be also good. Cancel. So what we get is exactly it's with this doohickey off aluminium. Upon register video of Cooper, I redid the entire square root. If you take the values from the table, we'll get it as 2.65 Hey Dennis to minus it. Or make. Which is that a distributor of aluminium on 1.7 to inter tenderness to minus 80 meter because they're the sooty off Quimper discredit of the same Don signature get is one point due for Hence we can state that very sure time. Me, too, off a new medium to copper. He's one point to who that will be. Our final answer

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