Calculating Resistance for a Wire with Different Dimensions

  • Thread starter Rowie25
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In summary, the resistance of a second wire, made of the same material, that is 1/4 as long and has 1/2 the diameter, is the same as the first wire. This is because a thick wire is like lots of thin wires in parallel, and a long wire is like lots of short wires in series. Therefore, the total resistance remains the same.
  • #1
Rowie25
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Homework Statement


A certain wire has a resistance of 78 Ω. What is the resistance of a second wire, made of the same material, that is 1/4 as long and has 1/2 the diameter?

I tried figuring out the equation and I ended up getting R2= 4p L1/4 divided by pi(d1/2)^2 and then I got that the resistance would be four times as great but that isn't correct. Please help! I'm not sure how to figure this out and it looks easy but I'm stuck. Thanks!
 
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  • #2
Do you know the difference between resistance and resistivity?
 
  • #3
I know that Resistance is voltage over current and resistivity of the material is E/J which the units are ohms *m right?
 
  • #4
Hi Rowie25! :smile:

Hint: a thick wire is like lots of thin wires in parallel, a long wire is like lots of short wires in series. :wink:
 
  • #5
Hmmm okay thank you! I'll try to figure it out.
 
  • #6
Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.
 
  • #7
Hi Rowie25! :smile:

(just got up :zzz: …)
Rowie25 said:
Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.

Yup! :biggrin:

1/4 the length, and 1/4 the area, so the total resistance is the same! :wink:
 
  • #8
Ohhh! Well it's actually 1/4 the length, 1/2 the diameter. So does that still make sense?
 
  • #9
1/2 the diameter = 1/4 the area :wink:
 
  • #10
Oh right right! I thought you wrote diameter. My bad! Thank you sooo much! :biggrin:
 

1. How do I find the unknown resistance of a circuit?

To find the unknown resistance of a circuit, you will need a known voltage source, an ammeter, and a voltmeter. First, connect the known voltage source to the circuit and measure the voltage using the voltmeter. Then, connect the ammeter in series with the unknown resistance and measure the current. Finally, use Ohm's law (R = V/I) to calculate the unknown resistance.

2. Can I use any voltage source to find the unknown resistance?

It is recommended to use a known voltage source with a stable output for accurate measurements. This can be a battery or a power supply. Using an unstable or fluctuating voltage source can affect the accuracy of your measurements.

3. How do I ensure the accuracy of my measurements?

To ensure the accuracy of your measurements, it is important to use high-quality equipment and follow proper measurement techniques. This includes using calibrated instruments, avoiding any external interference, and taking multiple measurements to calculate an average.

4. What if I don't have an ammeter or voltmeter?

If you do not have access to an ammeter or voltmeter, you can still find the unknown resistance by using a multimeter. Set the multimeter to measure current and voltage, and use the same steps as mentioned in the first question.

5. Is there a faster way to find the unknown resistance?

Yes, there are alternative methods such as using a Wheatstone bridge or a digital ohmmeter to find the unknown resistance. These methods may provide faster and more accurate results, but they require specialized equipment. It is recommended to use the method that is most suitable for your specific experiment or project.

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