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As shown in the figure, a current of 2 A passes through a conducting wire. The radius of the cross-section of the wire at point A is 3r and at point B is r. Find the ratio of the drift velocities at points A and B.

Asked in GUJCET 2021 · Drift velocity, mobility and current density

Figure: Drift velocity, mobility and current density
Answer: (3) 1/9

Step-by-step solution

Given: the same current I = 2 A at A and at B; radius 3r at A and r at B.

Idea: I = neAv_d, and n and e are the same all along the wire, so v_d∝1/A with A = π(radius)².

(v_A)/(v_B) = (A_B)/(A_A) = (π r²)/(π(3r)²).

(v_A)/(v_B) = 1/9.

So the drift velocities at A and B are in the ratio 1 : 9.

Why the other options are wrong

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