Difference Between Resistance and Resistivity

Resistance and resistivity are two fundamental concepts in the field of electricity. While they are related, they are not the same thing. Resistance is a measure of how much a material opposes the flow of electric current, while resistivity is a measure of how much a material resists the flow of electric current per unit length.

Resistance

Resistance is a measure of how difficult it is for electric current to flow through a material. It is measured in ohms (Ω). The higher the resistance, the more difficult it is for electric current to flow through the material.

The resistance of a material depends on several factors, including:

• Length: The longer the material, the higher the resistance.
• Cross-sectional area: The larger the cross-sectional area of the material, the lower the resistance.
• Material: The type of material also affects the resistance. Some materials, such as metals, have low resistance, while others, such as insulators, have high resistance.

Resistivity

Resistivity is a measure of how much a material resists the flow of electric current per unit length. It is measured in ohm-meters (Ω-m). The higher the resistivity, the more difficult it is for electric current to flow through the material.

The resistivity of a material is a fundamental property of the material. It does not depend on the length or cross-sectional area of the material.

Relationship Between Resistance and Resistivity

The resistance of a material is directly proportional to its resistivity and length, and inversely proportional to its cross-sectional area. This relationship can be expressed mathematically as follows:

$$ R = p * L / A $$

Where:

• R is the resistance in ohms (Ω)
• ρ is the resistivity in ohm-meters (Ω-m)
• L is the length of the material in meters (m)
• A is the cross-sectional area of the material in square meters (m²)

Resistance and resistivity are two important concepts in the field of electricity. Resistance is a measure of how difficult it is for electric current to flow through a material, while resistivity is a measure of how much a material resists the flow of electric current per unit length. The resistance of a material depends on its resistivity, length, and cross-sectional area.

Resistance and Resistivity Formulas

Resistance

Resistance is a measure of how difficult it is for an electric current to flow through a material. It is measured in ohms (Ω). The resistance of a material depends on its length, cross-sectional area, and resistivity.

The formula for resistance is:

$$ R = ρ * L / A $$

Where:

• R is resistance in ohms (Ω)
• ρ is resistivity in ohm-meters (Ωm)
• L is length in meters (m)
• A is cross-sectional area in square meters (m²)

Resistivity

Resistivity is a measure of how well a material resists the flow of electric current. It is measured in ohm-meters (Ωm). The resistivity of a material depends on its atomic structure and temperature.

The formula for resistivity is:

$$ ρ = R * A / L $$

Where:

• ρ is resistivity in ohm-meters (Ωm)
• R is resistance in ohms (Ω)
• A is cross-sectional area in square meters (m²)
• L is length in meters (m)

Temperature Dependence of Resistivity

The resistivity of most metals increases with temperature. This is because the increased temperature causes the atoms in the metal to vibrate more, which makes it more difficult for electrons to move through the material.

The formula for the temperature dependence of resistivity is:

$$ ρ = ρ₀ * [1 + α(T - T₀)] $$

Where:

• ρ is resistivity at temperature T in ohm-meters (Ωm)
• ρ₀ is resistivity at temperature T₀ in ohm-meters (Ωm)
• α is the temperature coefficient of resistivity in 1/°C
• T is temperature in °C
• T₀ is reference temperature in °C

Examples

The following table shows the resistivity of some common materials at room temperature:

As you can see, silver has the lowest resistivity of all the materials listed, while rubber has the highest. This means that silver is the best conductor of electricity, while rubber is the worst.

Facts About Resistance and Resistivity

Resistance

• Resistance is the opposition to the flow of electric current in a conductor.
• It is measured in ohms (Ω).
• The resistance of a conductor depends on its length, cross-sectional area, and material.
• The longer the conductor, the higher the resistance.
• The larger the cross-sectional area of the conductor, the lower the resistance.
• The more resistive the material, the higher the resistance.

Resistivity

• Resistivity is a measure of how resistive a material is to the flow of electric current.
• It is measured in ohm-meters (Ωm).
• The resistivity of a material is a constant that depends on the material’s atomic structure.
• The higher the resistivity of a material, the more difficult it is for electric current to flow through it.

Relationship Between Resistance and Resistivity

• The resistance of a conductor is directly proportional to its length and resistivity.
• The resistance of a conductor is inversely proportional to its cross-sectional area.

Applications of Resistance and Resistivity

• Resistance is used to control the flow of electric current in circuits.
• Resistivity is used to select materials for electrical components.

Examples of Resistance and Resistivity

• Copper has a low resistivity, so it is a good conductor of electricity.
• Rubber has a high resistivity, so it is a poor conductor of electricity.
• The resistance of a 1-meter long copper wire with a cross-sectional area of 1 square millimeter is approximately 0.017 ohms.
• The resistivity of copper is approximately 1.68 × 10$^{-8}$ ohm-meters.

Difference Between Resistance and Resistivity FAQs

What is resistance?

• Resistance is the opposition to the flow of electric current in a conductor. It is measured in ohms (Ω). The higher the resistance, the more difficult it is for current to flow.

What is resistivity?

• Resistivity is a measure of how much a material opposes the flow of electric current. It is measured in ohm-meters (Ωm). The higher the resistivity, the more difficult it is for current to flow through the material.

How are resistance and resistivity related?

• Resistance and resistivity are related by the following equation:

$$ R = ρL/A $$

• Where:
  • R is resistance in ohms (Ω)
  • ρ is resistivity in ohm-meters (Ωm)
  • L is the length of the conductor in meters (m)
  • A is the cross-sectional area of the conductor in square meters (m²)

What are some factors that affect resistance?

• The following factors can affect resistance:
  • The material of the conductor
  • The length of the conductor
  • The cross-sectional area of the conductor
  • The temperature of the conductor

What are some factors that affect resistivity?

• The following factors can affect resistivity:
  • The material of the conductor
  • The temperature of the conductor
  • The presence of impurities

Which is more important, resistance or resistivity?

• Both resistance and resistivity are important properties of conductors. Resistance is important for determining the current flow in a circuit, while resistivity is important for determining the material’s ability to conduct electricity.

Conclusion

Resistance and resistivity are two important properties of conductors. By understanding the difference between these two properties, you can better understand how electricity flows through materials.