Resistance
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Table of Contents
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Resistance
Key Definitions
Resistivity - a measure of resistance to flow of current within a material
- Good conductors have lower resistivity
- Good insulators have higher resistivity
Electrical Resistance - a measure of resistance to flow of current through a circuit
Ohm’s Law
, $\vec J$, depends on the applied
For linear materials the current density is proportional to the electric field given by Ohm’s Law:
\(\vec E=\rho\vec J\)
Where $\rho$ is the resistivity of the material given by:
\(\rho = \frac{E}{J}\)
Resistance (Alternate Form)
In the context of total current passing through a circuit, resistivity depends on shape/size and type of material, collectively defined as electrical resistance:
\(R=\frac{\rho L}{A}\)
Given :
\(V=IR\)
Temperature Dependance
Resistivity varies with many factors, but nearly all metallic conductors’ resistivity correlates with temperature:
\(\rho(T)=\rho_0[1+\alpha(T-T_0)]\)
Where $\rho_0$ is a reference resistivity at temperature $T_0$ known as the temperature coefficient of resistivity
Resistance (Alternate Form)
Similarly, temperature dependance is given by: