 # Resistivity Formula

Simply resistivity or Electrical resistivity is the resistance of the flow of current from one end to the other in a material. Electrical resistivity is a simply accessible and informative quantity to describe the material. It is the reciprocal of electrical conductivity. The resistivity is represented as ρ and it is directly proportional to the material resistance and length. Resistivity is inversely proportional to the area of cross-section of the given material.

## Formula of Resistivity

The resistivity formula is expressed as

$$\begin{array}{l}\rho = \frac{RA}{l}\end{array}$$

Where ρ is the resistivity, R is the resistance, l is the length of the material and A is the area of cross-section.

### Resistivity Solved Examples

Problem 1: Compute the resistivity of the given material whose resistance is 2 Ω; area of cross-section and length are 25cm2 and 15 cm respectively?

Given

R = 2 Ω

l = 15 cm = 0.15 m

A = 25 cm2 = 0.25 m2

Resistivity formula is

$$\begin{array}{l}\rho = \frac{RA}{l}\end{array}$$
$$\begin{array}{l}\rho = \frac{2\times 0.25}{0.15} = 3.333\ \Omega m\end{array}$$

Problem 2: The length and area of wire are given as 0.2 m and 0.5 m2 respectively. The resistance of that wire is 3 Ω, calculate the resistivity?

Given

R = 3 Ω

l = 0.2 m and

A = 0.5 m2

Resistivity formula is

$$\begin{array}{l}\rho = \frac{RA}{l}\end{array}$$
$$\begin{array}{l}\rho = \frac{3\times 0.5}{0.2} = 7.5\ \Omega m\end{array}$$

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