Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The…

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The ratio of their self inductance will be
  1. $1: 3$
  2. $1: 9$
  3. $9: 1$
  4. $3: 2$

Solution

$\mathrm{L} \propto \mathrm{r}^2$ and $\mathrm{L} \propto \frac{1}{l}$ $\begin{array}{ll} \therefore & \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{r}_1^2}{\mathrm{r}_2^2} \times \frac{l_2}{l_1} \\ \therefore & \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\frac{1}{9} \times \frac{3}{1}=\frac{1}{3} \end{array}$

Asked in: MHT CET 2024 (15 May Shift 1)

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