Power change in fixed resistor due to varying series resistance

Steps:

• Total resistance: internal 2Ω + X 40Ω + variable R (0 to 40Ω), so R_total = 42Ω to 82Ω.
• At R=0Ω, current I=12V/42Ω=2/7 A, power in X: (2/7)^2 × 40Ω = 160/49 W ≈3.27W.
• At R=40Ω, I=12V/82Ω=6/41 A, power in X: (6/41)^2 × 40Ω = 1440/1681 W ≈0.86W.
• Change in power: 160/49 - 1440/1681 ≈2.41W, rounds to 2.4W.

Why A is correct:

• Matches difference calculated using P=I²R formula for series circuit with internal resistance.

Why the others are wrong:

• B: Assumes no internal resistance, yielding 3.6W - 0.9W=2.7W.
• C: Equals maximum power in X (ignores variation).
• D: Overestimates by neglecting total resistance increase.

Final answer: A