What is Resistivity?
Resistivity (also called electrical resistivity) is a property of a material that tells us how strongly it opposes the flow of electric current. Unlike resistance, which depends on the shape and size of a specific wire or object, resistivity is a fixed property of the material itself — copper always has the same resistivity, regardless of whether it’s shaped into a thin wire or a thick rod.
Resistivity is represented by the Greek letter ρ (rho), and its SI unit is the ohm-meter (Ω·m). It is the reciprocal of electrical conductivity.
Resistivity Formula
Where:
- ρ = Resistivity of the material (Ω·m)
- R = Resistance (Ω)
- A = Area of cross-section (m²)
- l = Length of the material (m)
This can also be rearranged to find resistance directly:
Resistance vs Resistivity — Key Differences
Students often confuse these two related but different quantities:
| Point | Resistance (R) | Resistivity (ρ) |
|---|---|---|
| Definition | Opposition to current flow in a specific object | Opposition to current flow, as a material property |
| Depends on | Length, area, and material | Material and temperature only |
| Changes with shape/size? | Yes | No — stays the same regardless of shape |
| SI Unit | Ohm (Ω) | Ohm-meter (Ω·m) |
| Formula | R = V/I (Ohm’s Law) | ρ = RA/l |
Simple way to remember: Resistance is about a specific wire. Resistivity is about the material the wire is made of.
Factors Affecting Resistivity
- Type of material — metals like copper and silver have very low resistivity (good conductors); materials like rubber and glass have very high resistivity (insulators)
- Temperature — for most metals, resistivity increases as temperature rises, because atoms vibrate more and obstruct electron flow
- Impurities — adding impurities to a pure metal generally increases its resistivity
Why This Matters (Real-World Example)
This is exactly why copper is used for electrical wiring (very low resistivity → current flows easily, minimal energy loss), while nichrome (a nickel-chromium alloy with much higher resistivity) is used in electric heaters and toasters — its higher resistivity causes it to heat up when current passes through it, which is exactly the effect needed in a heating element.
Solved Examples
Example 1: Find the resistivity of a metal wire of length 2 m and diameter 0.6 mm, if its resistance is 50 Ω.
Given: R = 50 Ω, l = 2 m, diameter = 0.6 mm → radius = 3 × 10⁻⁴ m
Area of cross-section:
Now calculating resistivity:
Answer: ρ ≈ 7.065 × 10⁻⁶ Ω·m
Example 2: A copper wire has a resistivity of 1.68 × 10⁻⁸ Ω·m, length 5 m, and cross-sectional area 2 × 10⁻⁶ m². Find its resistance.
Given: ρ = 1.68 × 10⁻⁸ Ω·m, l = 5 m, A = 2 × 10⁻⁶ m²
Answer: R = 0.042 Ω
Example 3: Two wires are made of the same material. Wire A is twice as long as Wire B but has the same cross-sectional area. How do their resistances compare?
Since R = ρl/A, and ρ and A are the same for both wires, resistance is directly proportional to length.
Answer: Wire A will have twice the resistance of Wire B, even though both are made of the same material (same resistivity).
Frequently Asked Questions
Q1. What is the SI unit of resistivity? The SI unit of resistivity is the ohm-meter (Ω·m).
Q2. Does resistivity depend on the length or thickness of a wire? No. Resistivity is a fixed property of the material itself and does not change with the length or cross-sectional area — only resistance depends on those factors.
Q3. Why does resistivity increase with temperature in metals? As temperature rises, atoms in a metal vibrate more vigorously, which increases collisions with flowing electrons, making it harder for current to pass through — thus increasing resistivity.
Q4. What is the difference between resistivity and conductivity? Conductivity is the reciprocal of resistivity. Materials with low resistivity (like copper) have high conductivity, and materials with high resistivity (like rubber) have low conductivity.