Two circuits contain an emf produced by a moving metal rod, like that shown in 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 59 ?, and that in circuit 2 is 118 ?. 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?

(A) ?1/?2 = {.......}

(b)  I1/I2 = {.......}

(C)  P1/P2 ={.......}

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 59 ?, and that in circuit 2 is118 ?. 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

emf1 = emf2 = B*v*L*sin(90)

I1 = emf1/R = emf/59

I2 = emf2/R2 = emf/118

a) emf1/emf2 = 1

b) I1/I2 = 2

c) emf1 = B*2*v*L*sin(90)

emf2 = B*v*L*sin(90)


P1 = emf1^2/R1 = emf1^2/59

P2 = emf1^2/R2 = emf2^2/118


P1/P2 = (emf1/emf2)^2*118/59

P1/P2 = 8

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