A wire of cross-sectional area 2π  x  10$^-{8}$ m$^2$ and resistivity 1.1 x 10$^-{8}$ Ω m, has a resistance of 21Ω. Calculate the length of the wire. [π=22/7]

Concept: The resistance of a wire is given by R = ρL/A, so L = RA/ρ.

Given:

• R = 21 Ω
• A = 2π × 10⁻⁸ m², with π = 22/7
• ρ = 1.1 × 10⁻⁸ Ω m

Step 1: Find A A = 2 × (22/7) × 10⁻⁸ = (44/7) × 10⁻⁸ m²

Step 2: Substitute into L = RA/ρ L = (21 × (44/7) × 10⁻⁸) / (1.1 × 10⁻⁸)

The 10⁻⁸ terms cancel: L = (21 × 44/7) / 1.1 L = (3 × 44) / 1.1 L = 132 / 1.1 L = 120 m

Answer: C (120 m)

Tip: Simplify before multiplying. Here 21/7 = 3 made the arithmetic easy, and the powers of 10 cancelled. Always rearrange the formula first (L = RA/ρ) and cancel the common factors.