Resistance

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Table of Contents

• Resistance
  • Key Definitions
  • Ohm’s Law
    • $\overrightarrow{E}=\rho \overrightarrow{J}$
    • $\rho =\frac{E}{J}$
    • Resistance (Alternate Form)
      • $R=\frac{\rho L}{A}$
      • $V=IR$
  • Temperature Dependance
    • $\rho (T)={\rho }_0[1+\alpha (T-T_0)]$
    • Resistance (Alternate Form)
      • $R(T)=R_0[1+\alpha (T-T_0)]$

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Resistance

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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

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Ohm’s Law

, $\overrightarrow{J}$, depends on the applied

For linear materials the current density is proportional to the electric field given by Ohm’s Law:

$\overrightarrow{E}=\rho \overrightarrow{J}$

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 :

$V=IR$

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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:

$R(T)=R_0[1+\alpha (T-T_0)]$