Experiment shows that the resistance of a metallic conductor is directly proportional to the length of the wire and inversely proportional to the cross sectional area.

i.e, R∝LA∴R=ρLA

Hence, ρ=RAL

Where ρ the constant of the equation called the resistivity, expressed in ohm-meter (Ωm)

**Resistivity of a wire is defined as the product of the wire’s resistance and its cross sectional area, divided by the length of that wire. It can also be defined as the resistance of unit length of material of unit cross sectional area. It is the ability of a substance to restrict heat.**

If a wire has a diameter ** d**, then

A=πr2=πd24∴R=4ρLπd2andρ=πRd24L

**Conductivity on the other hand, is a measurement of the ability of a substance to conduct heat. It is the reciprocal of resistivity and denoted by σ**

Hence, σ=1ρσ=LRA=4LπRd2

**Example:**

A2m resistance wire, area of cross-section 0.50mm^{2}, has a resistance of 2.20Ω. Calculate

(a) the resistivity of the wire.

(b) the length of a wire which, when connected in parallel with the 2m wire will give a resistance of 2.0 Ω.

Solution:

(a) ρ=RALρ=2.2×0.5×10−62ρ=5.5×10−7Ωm

**EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):**

- Define resistivity.
- What is the relationship between resistivity and conductivity?
- What is a shunt?

**Join Discussion Forum and do your assignment**: Find questions at the end of each lesson, Click here to discuss your answers in the forum

**Ad: Get a FREE Bible**:
Find true peace. Click here to learn how you can get a FREE Bible.

**For advert placement/partnership, write [email protected]**

**Download our free Android Mobile application**:
Save your data when you use our free app. Click picture to download. No subscription.

**Tell your friends about Stoplearn.com. Click the share button below!**