Q152 / 160 · AP EAMCET 2024 (20 May Shift 2) · Physics
The ratio of the number of turns per unit length of two solenoids $A$ and $B$ is $1: 3$ and the lengths of $A$ and Bare in the ratio $1: 2$. If the two solenoids have same cross sectional area, the ratio of the self inductances of the solenoids A and B is
- A$1: 12$
- B$1: 6$
- Correct answerC$1: 18$
- D$1: 9$
Solution
For solenoids A and B ,
$\mathrm{n}_1: \mathrm{n}_2=1: 3, \mathrm{l}_1: \mathrm{l}_2=1: 2, \mathrm{~A}_1=\mathrm{A}_2$
Self inductance, $L=\mu_0 n^2 A 1 \Rightarrow L \mu n^2 1$ $\therefore \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\left(\frac{\mathrm{n}_1}{\mathrm{n}_2}\right)^2\left(\frac{\mathrm{l}_1}{\mathrm{I}_2}\right)=\left(\frac{1}{3}\right)^2\left(\frac{1}{2}\right)=1: 18$
Self inductance, $L=\mu_0 n^2 A 1 \Rightarrow L \mu n^2 1$ $\therefore \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\left(\frac{\mathrm{n}_1}{\mathrm{n}_2}\right)^2\left(\frac{\mathrm{l}_1}{\mathrm{I}_2}\right)=\left(\frac{1}{3}\right)^2\left(\frac{1}{2}\right)=1: 18$
Hence, the correct answer is option: 'C'.