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A2 Daily A Level Physics question

2026-07-05 OCR A Energy & power in DC circuits OCR-A Module 4.2.1 Energy, power and resistance OCR-A Module 4.2.2 I–V characteristics

A car headlamp bulb is rated 12 V, 55 W at normal operating temperature. In a lab test it is connected to a regulated 9.0 V DC supply. The filament’s resistance increases strongly with temperature. Which statement must be true about the power it dissipates at 9.0 V?

  1. A About 56% of 55 W, since power scales with V^2 for a fixed resistance.
  2. B Less than 56% of 55 W, because the filament runs cooler so its resistance is higher.
  3. C Greater than about 56% of 55 W but still less than 55 W, because cooling lowers the filament’s resistance. (correct)
  4. D Exactly 55 W, because a rated bulb draws whatever current it needs from any 9 V supply.

Answer

The correct answer is C.

Correct: C — Greater than about 56% of 55 W but still less than 55 W, because cooling lowers the filament’s resistance. A The 56% figure comes from assuming fixed resistance: (9/12)^2 ≈ 0.56; in reality the filament is cooler so R is lower and the power is higher than this estimate. B Cooler metal filaments have lower, not higher, resistance, so this predicts the wrong direction. C This is correct: at 9 V the filament is cooler so R < R_hot, giving P = 81/R > 81/R_hot ≈ 0.56×55 W, yet with a smaller voltage than 12 V the steady power must remain below 55 W. D A power rating is not enforced by the bulb; at 9 V it cannot dissipate 55 W because power depends on the applied voltage and the device’s I–V behaviour.

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