A2 Daily A Level Physics question
A bicycle bottle dynamo on a test rig produces an emf proportional to the wheel’s linear speed v. It powers an ohmic rear lamp of resistance 6 Ω; the dynamo’s internal resistance is 3 Ω. Ignore other losses. The horizontal force the dynamo exerts on the tyre is a drag (opposite the motion). When the speed is doubled from v to 2v, which statement must be true about (i) the power dissipated in the lamp and (ii) the magnitude of the drag force from the dynamo?
Answer
The correct answer is C.
Correct: C — Lamp power increases by a factor of 4; the drag force increases by a factor of 2. With emf ∝ v and total circuit resistance 6 Ω + 3 Ω = 9 Ω, the current I ∝ v. The lamp’s power is I^2×6 Ω ∝ v^2, so it quadruples when v doubles. The mechanical input power drawn by the dynamo is I^2×(6 Ω + 3 Ω) ∝ v^2, so the drag force magnitude is P_mech/v ∝ v and therefore doubles; it acts opposite the motion but the question asks for magnitude. A confuses force with power: while power ∝ v^2 (×4), force is power divided by speed, so it only doubles. B assumes power rises only in proportion to speed; since I ∝ v, the lamp’s power ∝ v^2, not v. C is correct for both the electrical and mechanical scaling, using the total circuit resistance for input power and P = Fv. D mixes the scalings, incorrectly linking a smaller increase in power with a larger increase in force.