Power proportional to current squared for fixed resistance

Steps:

• Original: P1 = I1²R = 2W, I1 = 3A, so R = 2 / 3² = 2/9 Ω.
• New power: P2 = 2W + 50% = 3W.
• I2²R = 3W, so I2² = 3 / (2/9) = 3 × 9/2 = 13.5.
• I2 = √13.5 ≈ 3.7A.

Why B is correct:

• P = I²R for fixed R means I ∝ √P; I2 = 3 × √(3/2) ≈ 3 × 1.2247 = 3.7A.

Why the others are wrong:

• A: 2.4A gives P = (2.4/3)² × 2 = 1.28W (decreases power).
• C: 4.5A gives P = (4.5/3)² × 2 = 4.5W (increases beyond 3W).
• D: 14A gives P = (14/3)² × 2 ≈ 43.5W (far too high).

Final answer: B