A potentiometer wire carries 0.2 A. Its resistivity is 4×10⁻⁷ Ω m and cross-sectional area 8×10⁻⁷ m². The potential gradient is k/10 V m⁻¹. Find k.
Physics · Mixed Chapter
JEE Mains

Question

A potentiometer wire carries 0.2 A. Its resistivity is 4×10⁻⁷ Ω m and cross-sectional area 8×10⁻⁷ m². The potential gradient is k/10 V m⁻¹. Find k.

G1 Physics · Accepted Answer

Step 1 — Resistance per unit length: For a uniform potentiometer wire, R/ℓ = ρ/A. Step 2 — Potential gradient: Potential drop per unit length is kₚ = I(R/ℓ) = Iρ/A. Step 3 — Substitute: I = 0.2 A; ρ = 4×10⁻⁷ Ω m; A = 8×10⁻⁷ m². kₚ = 0.2×4×10⁻⁷/(8×10⁻⁷) = 0.1 V m⁻¹. Step 4 — Compare with the question: 0.1 = k/10 ⇒ k = 1. Answer: 1.