Find the resistance of a wire (conductor)

In summary, the resistance of a wire is inversely proportional to its cross sectional area. If the diameter of the wire is halved, the cross sectional area is divided by 4 and the resistance becomes 4 times greater. This is because the surface area of the wire is proportional to its diameter squared.
  • #1
prishila
37
0

Homework Statement


If the diameter of a wire (conductor) is dimidiated , then its resistance:
A Remains unchangable
B is diminiated
C Becomes two times greater
D Becomes 4 times greater

Homework Equations


R=constant*length/Surface

The Attempt at a Solution


Cross sectional area=pi r^2=pi (D/2)^2=piD^2/4
Then the resistance becomes 4 times greater.
But in my book the answer is C.
 
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  • #3
Dr. Courtney said:
Is the surface area really proportional to r^2?
I think it is. Only if you consider pi to affect that
 
  • #4
Are you confusing surface area and cross sectional area?
 
  • #5
Dr. Courtney said:
Are you confusing surface area and cross sectional area?
Can you tell me the difference. in my book it says Resistance is in disproportional to the cross section of the resistance.
 
  • #6
prishila said:
Can you tell me the difference. in my book it says Resistance is in disproportional to the cross section of the resistance.
Surface area means area of the entire surface of the conductor. Cross sectional area is the area "through" which the current flows. Resistance is inversely proportional to the cross sectional area of the conductor.
 
  • #7
cnh1995 said:
Surface area means area of the entire surface of the conductor. Cross sectional area is the area "through" which the current flows. Resistance is inversely proportional to the cross sectional area of the conductor.
I understand. But how can this affect the solution of my exercise?
 
  • #8
prishila said:
I understand. But how can this affect the solution of my exercise?
If "dimidiated" means halved, I agree that the answer is D.
 

1. What is the definition of resistance?

Resistance is the measure of how difficult it is for electricity to flow through a material. In other words, it is the opposition to the flow of electric current.

2. How is resistance measured?

Resistance is measured in ohms (Ω) using a device called a multimeter. To measure the resistance of a wire, the wire is connected to the multimeter and the resistance reading is displayed on the screen.

3. What factors affect the resistance of a wire?

The resistance of a wire is affected by three main factors: the length, cross-sectional area, and material of the wire. Longer wires have higher resistance, while thicker wires have lower resistance. Different materials also have different resistances.

4. How does temperature affect the resistance of a wire?

In most materials, an increase in temperature leads to an increase in resistance. This is because as the temperature rises, the atoms in the material vibrate more, making it harder for electrons to pass through the material.

5. Why is it important to know the resistance of a wire?

Knowing the resistance of a wire is important in many practical applications, such as designing circuits and determining the safety of electrical systems. It also helps in understanding the behavior of electricity and how it flows through different materials.

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