Electric Circuits: Resistivity

Understanding Resistivity

Resistivity is a property that quantifies how strongly a material opposes the flow of electric current. It is a fundamental concept in the study of electric circuits.
Represented by the Greek symbol rho (ρ), resistivity is measured in ohm metres (Ωm).
It’s important to remember that resistivity depends on the properties of the material, not its shape or size.

Formula for Resistivity

The formula for resistivity is ρ = RA/L, where R represents resistance, A is the cross-sectional area of the material, and L is the length of the material.
The resultant units from this formula are ohm metres, consistent with the standard unit for resistivity.

Factors Affecting Resistivity

Temperature: As a general rule, resistivity increases with temperature for metallic conductors, and decreases with temperature for insulators and semiconductor materials.
Material composition: Different materials have different resistivity values. For example, copper has a low resistivity and is commonly used in electrical wiring, while rubber has a high resistivity and serves as an effective insulator.

Superconductivity

Superconductivity is a phenomenon where certain materials can exhibit zero electrical resistance and expulsion of magnetic fields when cooled below a certain temperature, known as the critical temperature.
Superconductors can carry a current indefinitely without any energy loss, which has significant implications for energy efficiency in electrical systems.

Ohm’s Law

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points. The equation for Ohm’s law is V = IR, where V represents voltage, I is current and R is resistance.
In the context of resistivity, resistance (R) can be expressed in terms of resistivity as R = ρL/A, which can be substituted into Ohm’s law for further analyses.

Resistors in Series and Parallel

In a series circuit, total resistance (R_total) is simply the sum of the individual resistances: R_total = R1 + R2 + … + Rn
In a parallel circuit, the inverse of total resistance is equal to the sum of the inverses of individual resistances: 1/R_total = 1/R1 + 1/R2 + … + 1/Rn

Remember, understanding resistivity is crucial in comprehending how electrical circuits function. Master the concept of resistivity and you will find the rest of electric circuits considerably more approachable.