What is Resistance & Resistivity?

What are resistors?

Resistors are the first of the three passive circuit elements you will be studying in this course.  Knowing how resistance is related to current and voltage is fundamental to analyzing a circuit.  Fortunately, it’s also one of the easiest concepts you will learn.

What is resistance?

Resistance (R) is a measure of how much a material prevents the flow of current and is measured in Ohms (Ω).  The resistance of a material depends largely on what the material is, but length and cross-sectional area also play a significant role.  These three factors are related to a material’s resistance by the following equation.

$R = \frac{\rho\ell}{A}$

Where ρ is the resistivity of the material (in Ω·m), ℓ is its length (in m), and A is its cross-sectional area (in m2).  From this equation, a wire’s resistance is doubled when its length is doubled.  In contrast, doubling the wire’s radius effectively divides its resistance by four.

What is resistivity?

Resistivity is a property of a material (not something that can be changed unless the material itself is changed).  Therefore, it plays the largest role in determining whether or not the material is a good conductor.  Silver, for example, has a resistivity of 1.6×10-8 Ω·m.  Meanwhile, wood has a resistivity of around 1014 Ω·m.  The disparity between these two resistivities is so great that length and cross-sectional area hardly matter; wood can never be a good conductor.  Note: While silver is a better conductor than copper, copper is used in wires because it’s much cheaper.  Written by Ryan Eatinger (reatinge@ksu.edu).  Thank you!