Question

Derive an equation of resistivity with respect to length and cross sectional area of conductor?

Answer 1

Explanation:

R=pL÷A

where p=resistivity

L=length

A= cross section area

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Answer 2

Answer:

The resistance R is definitely directly proportional to the length of the conductor. What this reflects is that resistance increases with an increase in the conductor’s length.

So, resistance (R) ∝ l (1)

The resistance R is certainly inversely proportional to the area of cross-section of a particular conductor. What this means is that R will decrease with an increase in the area of conductor and vice-versa. More area of the conductor leads to an efficient flow of electric current through more area and consequently decreases the resistance.

Therefore, resistance ∝ 1A of cross section of the conductor (A)

Or, R ∝ 1A (2)

Now from equation (1) and (2)

R ∝ lA

Or, R = plA (3)

Here ρ (rho) happens to be the proportionality constant. Most noteworthy, it is the electrical resistivity of the material of conductors.

Now from equation (3)

RA = ρl

Or its alternate can be, ρ = RAl

Explanation: