Relationship Between Resistivity and Conductor Dimensions

In summary, resistivity is a measure of a material's ability to resist the flow of electricity and is directly related to a cylinder's shape, size, and material composition. It can be calculated using the formula ρ = RA/l, and is affected by factors such as the material, length, cross-sectional area, and temperature. Resistivity and conductivity are inversely related and are affected by the same factors, but are measured and expressed differently. This concept is important in understanding the behavior of materials when electricity is passed through them, which is crucial in designing and using electrical and electronic devices.
  • #1
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Homework Statement


A cylindrical conductor of length l, diameter D and resistivity ρ has resistance R. A different
cylindrical conductor of resistivity 2ρ, length 2l and diameter 2D has a resistance

A. 2R.
B. R.
C. R/2.
D. R/4



Homework Equations



I assume its R = pL/A


The Attempt at a Solution



I tried putting 2p2L/2A into the equation getting 4/2 = 2 then dividing both sides by 2 to give R/2 but apparently the answer should be B. R? Not sure how?
 
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  • #2
The cross sectional area is proportional to the square of the diameter.
 

What is resistivity and how is it related to a cylinder?

Resistivity is a measure of a material's ability to resist the flow of electricity. In the case of a cylinder, resistivity is directly related to the cylinder's shape, size, and material composition.

How is resistivity calculated for a cylinder?

The resistivity of a cylinder can be calculated using the formula ρ = RA/l, where ρ is the resistivity, R is the resistance, A is the cross-sectional area of the cylinder, and l is the length of the cylinder.

What factors affect the resistivity of a cylinder?

The resistivity of a cylinder can be affected by factors such as the material it is made of, its length and cross-sectional area, and the temperature at which it is being measured.

How does resistivity differ from conductivity in a cylinder?

Resistivity and conductivity are inversely related to each other. This means that a material with high resistivity will have low conductivity and vice versa. In a cylinder, resistivity and conductivity are affected by the same factors, but they are measured and expressed differently.

Why is resistivity important in the study of electricity and materials?

Resistivity is an important concept in the study of electricity and materials because it helps us understand how different materials behave when electricity is passed through them. This knowledge is crucial in designing and using various electrical and electronic devices.

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