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An aluminum bar 3.80 $\mathrm{m}$ long has a rectangular cross section 1.00 $\mathrm{cm}$ by 5.00 $\mathrm{cm} .$ (a) What is its resistance? (b) What is the length of a copper wire 1.50 $\mathrm{mm}$ in diameter having the same resistance?

the length of the copper wire is $[2.05 \mathrm{cm}]$

Physics 102 Electricity and Magnetism

Chapter 19

Current, Resistance, and Direct-Current Circuit

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Kharell J.

September 24, 2021

An aluminum bar 3.80 long has a rectangular cross section 1.00 by 5.00 (a) What is its resistance? (b) What is the length of a copper wire 1.50 in diameter having the same resistance?

University of Michigan - Ann Arbor

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in the first part of this problem, we are going to call clear resistance up aluminum. What have England off? Three point and zero meter and rectangular area position. Wants it to me to buy five centimeter. So he had real lend equal toe tree pine and zero meter area off procession equal toe once into media buy five scenting meteo. So the hell area equal to five centimeters to care are we can ride this in a signers is five times 10 to the power minus for Secare meter. No. Why? Using the delusion reticence equal toe resist city off the material times Linda brought upon area off position off the road now by putting different values here with this duty for aluminum is do plan 63 times tend to the lower minus and one meter lint off the roadies she might Angela Mita and area after a session of the road is five times 10 to the power minus for secure meter. So we get our equal to 1.99 at at times 10 to the power minus for Oh, our recon approximately says are equal to 2.0 times 10 to the power minus for home? No. In the second part of this problem, we want to complete lend up a copper wire having Demeter off 1.50 millimeter and resistance equal to the citizens of the road given up problem 11 and part air. So here in problem 11 party, we have resistance equal to group. They sense equal toe 1.998 10 times 10 to the power minus for well, um, and die Mission Off the wire is 1.50 millimeter. So radius are wired. It is half up the imager There is zero point 75 millimeter which is a little 0.75 times 10 to the power minus three meter. Now again, by using the relation, are equal to really study time's lend upon radio cross section. So by rear ending the hell relation for lend is l physical do ready sense times area off position upon this dirty it's a very oppositional wire is fight I'm pi times our secure So we have our indu hear area processional white is buy into So get all radius upon this duty No, by putting different values in the relation here. Reticence off The wire is 1.99 and dent times 10 to the power minus four room. The value of Phi Phi is 3.14 and ready? Yes. Here is zero point 75 times. Tend to the bower minus stream. Media of one. Where you off row then? Released duty Far Cooper is 1.72 times. Tend to the bar on minus and or meter. So by computing, we have a value Far l It was due 2.5 times 10 to the hour minus two are we can write This s lend equal to group iron 05 sent in Mito their sponsor. Thanks for watching.

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