The Physics of Resistance
Electrical resistance is the measure of the opposition to the flow of electric current in a conductor. Unlike Ohm's Law, which relates resistance to voltage and current, this calculator focuses on the physical properties of the material itself.
The resistance ($R$) of a wire depends on three primary factors:
- Resistivity ($\rho$): An intrinsic property of the material. Silver and copper have extremely low resistivity, while insulators like rubber have near-infinite resistivity.
- Length ($L$): Resistance is directly proportional to length. A longer wire provides more "friction" for moving electrons.
- Cross-sectional Area ($A$): Resistance is inversely proportional to area. A thicker wire (larger $A$) is like a wider highway, allowing more current to flow with less resistance.
The Formula
Where:
R=
Resistance (Ohms, Ω)=
Resistivity (Ohm-meters, Ω·m)L=
Length (meters, m)A=
Cross-sectional Area (m²)Example Calculation
You have a copper wire ($\rho = 1.68 \times 10^{-8} , \Omega\cdot\text{m}$) that is $10 , \text{meters}$ long and has a cross-sectional area of $2 , \text{mm}^2$ ($2 \times 10^{-6} , \text{m}^2$).
- Multiply Resistivity by Length: $(1.68 \times 10^{-8}) \times 10 = 1.68 \times 10^{-7}$.
- Divide by Area: $(1.68 \times 10^{-7}) / (2 \times 10^{-6}) = 0.084 , \Omega$.
The total resistance of the wire is $0.084 , \Omega$.