wo circuits contain an emf produced by a moving metal rod, like that shown in th

Question

wo circuits contain an emf produced by a moving metal rod, like that shown in the drawing. The speed of the rod is the same in each circuit, but the bulb in circuit 1 has one-half the resistance of the bulb in circuit 2. The circuits are otherwise identical. The resistance of the light bulb in circuit 1 is 57 , and that in circuit 2 is 114 . Determine (a) the ratio 1/2 of the emfs and (b) the ratio I1/I2 of the currents 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 powers in the circuits?

Explanation / Answer

Two circuits contain an emf produced by a moving metal rod, like that shown in the drawing. The speed of the rod is the same in each circuit, but the bulb in circuit 1 has one-half the resistance of the bulb in circuit 2. The circuits are otherwise identical. The resistance of the light bulb in circuit 1 is 57 , and that in circuit 2 is 114 .

Determine
(a) the ratio 1/2 of the emfs
k1 = 1/2 = 1.00
(b) the ratio I1/I2 of the currents in the circuits
k2 = (1/57)/(1/114) = 114/57 = 2.00
(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 powers in the circuits?
speed V
k3 = ((2)^2/R)/(^2/2R) = 4*2=8 w

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