Two circuits contain an emf produced by a moving metal rod. The speed of the rod

Question

Two circuits contain an emf produced by a moving metal rod. The speed of the rod is the same in each circuit but the bulb in circuit 1 has one-half the resisitance of the bulb in curcuit 2. The circuits are otherwiase indentical. The resisitance of thelight bulb in curcuit 1 is 55 and that in circuit 2 is 110. Determine, (a) the ratio 1/2 of the emfs and (b) the ratio I1/I2 of the current in the circuits. (c) if the speed of the rod in circuit 1 were twice that in circuit 2 , what would be the ratio P1/P2 of the power in the circuits.

Explanation / Answer

(a) When two circuits are contianing the smae speed of rod then the emf produced in each circuit is motional emf                   = BLv so the motional emf is independent of resistance therefore the ratio                 1 / 2 = 1: 1 (b) The induced current             I = /R then            I1 / I2 = (1/R1) / (2 / R2)                      = (1 / 2) (R2/R1)                      = 110 / 55 = 2 (c) If the speed of the rod in circuit 1 is twice i.e v1 = 2v1 then the power              P1 / P2 = (1^2 /R1) / (2^2 / R2)                          = [( BL2v)^2/ (BLv)^2 ] (R2/ R1)                           = 4 (2) = 8

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