Resistivity MCQs Quiz | Class 10

Understanding Resistivity: A Deeper Dive

Resistivity is a fundamental property of a material that quantifies how strongly it resists the flow of electric current. Unlike resistance, which depends on the dimensions (length and cross-sectional area) of a specific object, resistivity is an intrinsic characteristic of the material itself, much like its density or melting point.

Definition of Resistivity (rho)

Resistivity (rho, ρ) is defined by the formula:

R = ρ * (L / A)

Where:

• R is the resistance of the conductor (in Ohms)
• ρ is the resistivity of the material (in Ohm-meters)
• L is the length of the conductor (in meters)
• A is the cross-sectional area of the conductor (in square meters)

From this formula, if we consider a conductor of unit length (1 meter) and unit cross-sectional area (1 square meter), then its resistance R will be equal to its resistivity ρ. This means resistivity is the resistance offered by a unit cube of the material.

Resistivity as a Material Property

Resistivity is solely dependent on the nature of the material and its temperature. It does not change with the shape or size of the object made from that material. For example, a long thin copper wire and a short thick copper wire will have different resistances, but the resistivity of the copper material itself remains the same for both at the same temperature.

The value of resistivity helps us classify materials:

• Conductors: Have very low resistivity (e.g., metals like copper, silver, aluminum, 10^-8 to 10^-6 Ohm-meter). They allow current to flow easily.
• Semiconductors: Have intermediate resistivity (e.g., silicon, germanium, 10^-5 to 10^0 Ohm-meter). Their resistivity can be controlled.
• Insulators: Have very high resistivity (e.g., glass, rubber, wood, 10^10 to 10^17 Ohm-meter). They strongly resist current flow.

Unit Concept: Ohm-meter

Let’s derive the SI unit of resistivity:

From the formula: R = ρ * (L / A)

We can rearrange it to find ρ:

ρ = (R * A) / L

Substituting the SI units for each quantity:

• R (Resistance) is in Ohms (Ω)
• A (Area) is in square meters (m²)
• L (Length) is in meters (m)

So, the unit of ρ becomes: (Ω * m²) / m = Ω * m.

Therefore, the SI unit of resistivity is Ohm-meter (Ωm).

Effect of Temperature

For most metallic conductors, resistivity increases with an increase in temperature. This is because higher temperatures cause atoms to vibrate more vigorously, leading to more frequent collisions with electrons, thus hindering current flow. For semiconductors, resistivity generally decreases with an increase in temperature.

Resistivity Values for Common Materials

Quick Revision Points

• Resistivity is an intrinsic property of a material.
• It depends on the nature of the material and its temperature.
• Its SI unit is Ohm-meter (Ωm).
• Resistivity distinguishes conductors (low), semiconductors (moderate), and insulators (high).
• For metals, resistivity generally increases with temperature.
• Alloys typically have higher resistivity than pure metals and are less sensitive to temperature changes.

Practice Questions

1. Why is nichrome alloy often used in heating elements instead of pure metals?
2. How does the resistivity of a semiconductor change as its temperature increases?
3. If you have two wires of the same material and length, but one is twice as thick as the other, which one will have lower resistance, and how does their resistivity compare?
4. Name two factors that resistivity depends on.
5. Explain why resistivity is considered a fundamental property of a substance, unlike resistance.