Ohm's Law and Wire Resistance

Steps:

• Potential difference V = I R, where I is constant current.
• Resistance R = ρ L / A, with ρ constant resistivity, L length, A cross-sectional area.
• For constant I, V is proportional to R.
• R increases with L and decreases with A (A = π (d/2)^2, so inversely with diameter d squared).

Why A is correct:

• From R = ρ L / A, V = I ρ L / A, so V ∝ L for constant I, ρ, and A.

Why the others are wrong:

• B: V increases with L, not decreases.
• C: V decreases as diameter increases (larger A lowers R).
• D: V inversely proportional to d squared, not d.

Final answer: A