## What is Resistivity?

**Resistivity Formula and Definition:** Resistivity is a physical property of materials that describes their ability to resist the flow of electric current. **It is typically measured in units of ohm-meters (Ωm)**. It is determined by the material’s length, Area, and resistance or temperature.

Materials with high resistivity impede the flow of electric current more than materials with low resistivity. Resistivity is an important property in the design and use of electrical and electronic components and systems.

**The formula for calculating resistivity **is

**ρ = (R x A) / L**

Where

ρ = Resistivity

R = Resistance

A = Area

L = Length

## Resistivity Practice Problems

Here are a few solved problems on resistivity of a metal

### Problem 1

Calculate the resistivity of a wire length 4m and cross-sectional area 4×10^{-7}m^{2} if its resistance is 3.0 ohms.

[UTME 2019]

**Solution**

**Data:** To calculate the resistivity of a wire, the first step is to bring out the data from the question above

As we can see,

Length of the wire (L) = 4m

Cross-sectional Area (A) = 4×10^{-7}m^{2}

Resistance of the wire (R) = 3Ω

Resistivity of the wire (ρ) = ?

The formula is given as

ρ = (RA) / L

Therefore, by substituting the values of ρ, R and L into the above equation, we will have

ρ = ( 3 x 4×10^{-7}) / 4

The above expression will give us

ρ = 0.0000012 / 4

Therefore, the resistivity of a wire is

ρ = 0.0000003

ρ = 3×10^{-7}Ωm

Hence, the resistivity of the wire is 3×10^{-7}Ωm

### Problem 2

What is the resistivity of a cylindrical material wire whose 1.0 meters length has a resistance of 2.0 ohms? The diameter of the wire is 0.5 millimeters.

**Answer**

**The final answer to the above question is 3.93 x 10 ^{-7} ohm – meter**

**Explanation**

L = 1.0 m

r = d/2 = 0.5 / 2 = 0.25 mm

We can now covert r into meters

r = 0.25 mm = 0.25/1000 = 2.5 x 10^{-4} m

A = πr^{2} = 3.142 x ( 2.5 x 10^{-4})^{2} = 2 Ω

Since ρ = (R x A) / L

ρ = (2 x 3.142 x 2.5 x 10^{-4})^{2} / 1

ρ = 3.93 x 10^{-7} Ωm

**Therefore, the resistivity of the cylindrical material is 3.93 x 10 ^{-7} ohm – meter**

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