A-LevelPhysicsD.C. circuits9702/21 · Oct/Nov 2017 · Q710 Marks

Wires are used to connect a battery of negligible internal resistance to a lamp, as shown in Fig. 7.1. The lamp is at its normal operating temperature. Some data for the filament wire of the lamp and for the connecting wires of the circuit are shown in Fig. 7.2. [Figure 7.1] [Figure 7.2]

(a)Define the ohm.[1]
(b)(i)Show that resistance of filament wire / total resistance of connecting wires = 1000.[2]
(b)(ii)Use the information in (i) to explain qualitatively why the power dissipated in the filament wire of the lamp is greater than the total power dissipated in the connecting wires.[1]
(b)(iii)The lamp is rated as 12V, 6.0W. Use the information in (i) to determine the total resistance of the connecting wires.[3]
(b)(iv)The diameter of the connecting wires is decreased. The total length of the connecting wires and the resistivity of the metal of the connecting wires remain the same. State and explain the change, if any, that occurs to the resistance of the filament wire of the lamp.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[B1] (the ohm is) volt / ampere
[C1] R = ρL/A
[A1] ratio = [ρL/(πd²/4)] / [0.028ρ × 7.0L / {π(14d)²/4}] = 1000 or ratio = 14² / (0.028 × 7) = 1000
[B1] same current (in connecting and filament wires) and the lamp/filament (wire) has greater resistance
[C1] P = V²/R or P = VI or P = I²R
[C1] (for filament wire) R = 12²/6.0 or R = 6.0/0.50² or R = 12/0.50
[A1] (for filament wire) R = 24Ω (for connecting wire) R = 24 / 1000 = 2.4 × 10⁻²Ω
[B1] resistance of connecting wire increases
[M1] current in circuit/lamp/filament (wire) decreases or potential difference across lamp/filament (wire) decreases
[A1] (so) resistance of lamp/filament (wire) decreases

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