Doubling Resistance of 1 Mile Copper Wire - 68 ohms

In summary, when a 1 mile long copper wire with a resistance of 68 ohms is doubled over and used as "one" wire, its new resistance will be 17 ohms. This is because resistance is inversely proportional to the cross-sectional area and directly proportional to the length, resulting in a 1/4 decrease in resistance.
  • #1
dymand68
21
0

Homework Statement


A 1 mile long copper wire has a resistance of 68 ohms. What will be its new resistance when doubling it over and using it as "one" wire



Homework Equations

?
R=V/current



The Attempt at a Solution

unable to attempt, I know that when it is cut in half R=34 ohms
 
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  • #2
dymand68 said:
I know that when it is cut in half R=34 ohms
OK. More generally, how does resistance depend on length and cross-sectional area?
 
  • #3
inverse square rule?
 
  • #5
the correct answer is 17 ohms...double width, 1/2 length =1/4 resistance?
 
  • #6
dymand68 said:
the correct answer is 17 ohms...double width, 1/2 length =1/4 resistance?
That's right. As that site explains, the resistance is inversely proportional to the cross-sectional area (which gives one factor 1/2) and directly proportional to the length (which gives a second factor of 1/2).
 

FAQ: Doubling Resistance of 1 Mile Copper Wire - 68 ohms

1. What does it mean to double the resistance of a 1 mile copper wire?

Doubling the resistance of a 1 mile copper wire means increasing its resistance by a factor of two. This means that it will require twice as much voltage to produce the same amount of current through the wire.

2. How is resistance measured in a copper wire?

Resistance is measured in ohms, which is a unit of electrical resistance. In a copper wire, resistance is determined by the length, cross-sectional area, and temperature of the wire.

3. Why would one want to double the resistance of a copper wire?

There are several reasons why one may want to double the resistance of a copper wire. One reason could be to increase the voltage drop in a circuit, which can be useful in certain applications. Another reason could be to reduce the amount of current flowing through the wire, which can help prevent overheating and damage to the wire.

4. Can the resistance of a copper wire be doubled without changing its length or temperature?

Yes, the resistance of a copper wire can be doubled without changing its length or temperature by altering the wire's cross-sectional area. This can be done by either doubling the thickness of the wire or by using a wire with a different gauge.

5. How can one double the resistance of a 1 mile copper wire?

To double the resistance of a 1 mile copper wire, one can either double the thickness of the wire or use a wire with a larger gauge. These methods will increase the cross-sectional area of the wire, resulting in a higher resistance. It is important to note that doubling the resistance will also affect the wire's electrical conductivity and heat dissipation capabilities.

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