The formula for resistivity is: &#x03C1;<!-- ρ --> = R A </mro

Esmeralda Lane 2022-07-13 Answered
The formula for resistivity is:
ρ = R A L
where ρ is resistivity, R is resistance, A is cross-sectional area, and L is the length of the conductor.
We can see from the formula that A and L are involved, why then does resistivity not depend on dimensions?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Jayvion Mclaughlin
Answered 2022-07-14 Author has 14 answers
It's because resistance ( R) is also a function of size.
A short and wide section of a material will have lower resistance than a long thin section of the same material. Larger cross sections have less resistance, and longer conductors have more resistance.
Therefore, by multiplying resistance by area and dividing by length, you get a value for a material property (resistivity ρ) that doesn't depend on the size of the conductor.
That is the point of resistivity, to be applicable to a material over various cross sections and lengths.
Not exactly what you’re looking for?
Ask My Question
Lucian Maddox
Answered 2022-07-15 Author has 8 answers
True, A and L are involved. But resistivity is a constant.
In the equation
ρ = R A L
if you change the resistance and length of conductor and then experimentally measure the resistance, and put it in the formula, you'll find that the resistivity has remained a constant for all different A and L, because R gets suitable modified to keep resistivity constant.
This is an experimental result. I remember trying this out myself, and the results showed that resistivity is a constant.
For another example, consider this formula for Coloumb's law:
F = 1 4 π ϵ 0 q 1 q 2 r 2
where ϵ 0 is the permittivity of free space. Now, you can aptly write
ϵ 0 = 1 4 π F q 1 q 2 r 2
and say that it is not a constant. But experiments show that for different values of q 1 , q 2 and r, the force F varies such that permittivity ϵ 0 remains a constant for a particular material, at a particular temperature.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-04-25

Flux through a Cube (Eigure 1) A cube has one corner at the origin and the opposite corner at the point (L, L, L). The sides of the cube are parallel to the coordinate planes image
image

asked 2022-04-07
If a current of 5A passing through a circuit generates 450W of power, what is the resistance of the circuit?
asked 2022-05-15
What is the statement of Ohm's Law?
asked 2022-05-18
What will be the area which is bounded by x = 0 , y = π / 4 and y = arctan ( x )?
asked 2022-05-10
What is the strength of the electric field at the position indicated by the dot in the figure?
photo
What is the strength of the electric field at the position indicated by the dot in the figure?
E = ¯ N C
What is the direction of the electric field at the position indicated by the dot in the figure? Specify the direction as an angle above the horizontal line.
θ = ¯ .
asked 2022-07-20
The length of the material can be measured with a ruler or caliper, and its resistance with an ohmmeter. Knowing these values, it is possible to calculate the resistivity of the material ? on:
?= R A/L
(a) What will happen to the material’s resistivity if the resistance is increased?
(b) What will happen to the material’s resistivity if the length is increased?
asked 2022-05-13
What is the electric current produced when a voltage of 9V is applied to a circuit with a resistance of 99 Ω?

New questions