Ohm's Law and Wire Resistance

Steps:

• Ohm's law states V = IR; with V constant, I ∝ 1/R.
• Resistance R = ρl / A, where ρ is resistivity (constant for same metal) and A is cross-sectional area.
• Area A = π(d/2)² ∝ d².
• Thus, R ∝ l / d², so I ∝ d² / l.

Why D is correct:

• D states I is inversely proportional to l and directly to d², matching I ∝ d² / l from the resistance formula R = ρl / A with A ∝ d².

Why the others are wrong:

• A: Current decreases with l (inversely), not increases (directly).
• B: Current decreases with l (inversely), not increases (directly).
• C: Current increases with d² (directly), not d (directly).

Final answer: D