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Two circuits contain an emf produced by a moving metal rod, like that shown in t

ID: 1445341 • Letter: T

Question

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 46 , and that in circuit 2 is 92 . 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

a) Setup is same for both circuit except bulb.

and induced emf, e = B L v   = same   (no R in there)

so e1/e2 = 1

b) I = e/R

I1/I2 = (e /46) / (e/92) =2


c) when speed is twince in 1

then e1 = 2BLv and e2= BLv

e1= 2e2

P = e^2 / R

P1/P2 = ( e1^2 / 46 ) / (e2^2 / 92) = (4 e2^2 /46) / (e2^2 / 92)

      = 8

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