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AIIMS 2013
Exam
AIIMS
Year
2013
Subject
Physics
Chapter
Electromagnetic Induction

AIIMS 2013 · Physics · Electromagnetic Induction

Two solenoids of equal number of turns having their length and the...

Two solenoids of equal number of turns having their length and the radii in the same ratio 1:21: 2. The ratio of their self-inductance will be

Options

  1. A1:21: 2
  2. B2:12:1
  3. C1:11:1
  4. D1:41:4

Correct answer

A. 1:21: 2

Step-by-step solution

For solenoids, self inductance is given by, L=μ0N2AlL=\frac{\mu_0 N^2 A}{l} ∴L1L2=(πr12l1)(πr22l2)=(r12l1)(r22l1)\therefore \quad \frac{L_1}{L_2}=\frac{\left(\frac{\pi r_1^2}{l_1}\right)}{\left(\frac{\pi r_2^2}{l_2}\right)}=\frac{\left(\frac{r_1^2}{l_1}\right)}{\left(\frac{r_2^2}{l_1}\right)} or L1L2=12(∵r12l1/r22l2=1/2)\quad \frac{L_1}{L_2}=\frac{1}{2} \quad\left(\because \frac{r_1^2}{l_1} / \frac{r_2^2}{l_2}=1 / 2\right)
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