Power-voltage relationship in resistors

Steps:

• Initial power P = V²/R = 5 W, so R = V²/5 Ω.
• New energy E = 50 J in t = 2.5 s, so new power P' = E/t = 50/2.5 = 20 W.
• New pd = V', so P' = V'²/R = 20 W.
• Substitute R: 20 = V'²/(V²/5), so V'²/V² = 4, V' = 2V.

Why B is correct:

• Power P ∝ V² for fixed R; new P' = 4 × initial P requires V' = √4 × V = 2V.

Why the others are wrong:

• A: ½V gives P' = (1/4)×5 = 1.25 W, E = 3.125 J (too low).
• C: 3V gives P' = 9×5 = 45 W, E = 112.5 J (too high).
• D: 4V gives P' = 16×5 = 80 W, E = 200 J (too high).

Final answer: B