Hand-cranked generator and a parallel-resistor circuit
In a science club at a Tottori junior high school, students build a hand-cranked generator. A coil of 200 turns is connected to a galvanometer. A bar magnet is pushed into the coil at 0.20 m/s, and the needle deflects to the right by 3 divisions. Pulling the magnet out at the same speed deflects it to the left by 3 divisions. Pushing in at 0.40 m/s gives 6 divisions. The students then replace the coil with one of 400 turns and push the magnet in at 0.20 m/s. Separately, they connect a 6.0 V battery to a 10 Ω resistor and a 15 Ω resistor in parallel, with an ammeter in the main branch. One student claims the total resistance is 25 Ω. The teacher asks them to justify each prediction with a rule, not just a number.
1. Predict the galvanometer deflection when the 400-turn coil is used with the magnet pushed in at 0.20 m/s, and state the direction when the magnet is pulled out. Justify your answer with a physics rule.
Read the worked answer
The deflection should be 6 divisions to the right. The induced emf depends on the rate at which the magnetic flux through the coil changes and on the number of turns. Changing from 200 to 400 turns doubles the induced emf for the same magnet speed, so 3 divisions becomes 6 divisions. When the magnet is pulled out, the flux through the coil decreases instead of increases, so the direction of the induced current reverses. The needle therefore deflects to the left. This is consistent with Lenz's law: the induced current produces a magnetic field that opposes the change in flux. The magnitude at the same speed would again be 6 divisions because the 400-turn coil is still being used.
2. Calculate the total resistance and the main current in the parallel circuit. Explain why 25 Ω cannot be correct.
Read the worked answer
For resistors in parallel, 1/R = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so R = 6.0 Ω. The main current is I = V/R = 6.0/6.0 = 1.0 A. The value 25 Ω is the sum of 10 Ω and 15 Ω, which is the rule for a series connection, not a parallel one. A parallel combination must have a total resistance smaller than the smallest branch resistance, so 6.0 Ω is reasonable and 25 Ω is impossible. With 25 Ω, the main current would be only 0.24 A, which contradicts the parallel-circuit rule that adding a branch provides another path and lowers the total resistance.
3. The magnet is held still inside the coil. Predict the galvanometer reading and explain your reasoning.
Read the worked answer
The reading should be zero. An induced emf is produced only while the magnetic flux through the coil is changing. If the magnet is stationary, the flux is constant, so the rate of change of flux is zero and no current is induced. The fact that a strong magnetic field may be present inside the coil does not matter by itself; electromagnetic induction depends on change, not on the absolute size of the flux. This also explains why the needle returns to zero when the motion stops after the magnet has been pushed in or pulled out.