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The self-inductances of two solenoids A and B of equal length are the same. The numbers of turns in solenoids A and B are 100 and 200 respectively. The ratio of the radii of their cross-sections, r_A:r_B, will be _____.

Asked in GSEB Board July 2017 · Coil geometry, cores and combinations

• (1) 2:1
• (2) 1:2
• (3) 1:4
• (4) 4:1

Step-by-step solution

Why the other options are wrong

• (2) Takes the radius as growing with the number of turns, r_A:r_B=100:200. For equal inductance the relation is inverse: the solenoid with more turns must be thinner.
• (3) Squares the direct turns ratio, ((100)/(200))²=1/4. Both the square and the direction are wrong for radii: r goes as 1/N.
• (4) This is the ratio of the cross-sectional areas, ((200)/(100))²=4:1. The radii are in the square root of that ratio.

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