Calculate the resistivity of the material of a wire of length 1 m, radius 0.01 cm and resistance 20 ohms.

646 views 62 helpful Updated May 31, 2025
Appears in Class 10th
Solution ✔ Verified
Answer

To calculate the resistivity (ρ) of the material, we use the formula:

R = ρ × (L / A)

Where:

  • R = 20 ohms (resistance)
  • L = 1 meter (length)
  • A = πr² (cross-sectional area of the wire)
  • r = 0.01 cm = 1 × 10⁻⁴ meters (radius)

Step-by-step calculation:

Calculate the area (A) of the wire's cross section:
A = π × (1 × 10⁻⁴)² = π × 10⁻⁸ m² ≈ 3.1416 × 10⁻⁸ m²

Rearrange the formula to solve for ρ:
ρ = R × (A / L)

Substitute the values:
ρ = 20 × (3.1416 × 10⁻⁸ / 1)

Calculate the resistivity:
ρ ≈ 20 × 3.1416 × 10⁻⁸ = 6.28 × 10⁻⁷ Ω·m

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