MHT CET · Physics · Electromagnetic Induction
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
- A \(1: 3\)
- B \(1: 9\)
- C \(9: 1\)
- D \(3: 2\)
Answer & Solution
Correct Answer
(A) \(1: 3\)
Step-by-step Solution
Detailed explanation
\(\mathrm{L} \propto \mathrm{r}^2\) and \(\mathrm{L} \propto \frac{1}{l}\)
\(\begin{array}{ll}
\therefore & \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{r}_1^2}{\mathrm{r}_2^2} \times \frac{l_2}{l_1} \\
\therefore & \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\frac{1}{9} \times \frac{3}{1}=\frac{1}{3}
\end{array}\)
\(\begin{array}{ll}
\therefore & \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{r}_1^2}{\mathrm{r}_2^2} \times \frac{l_2}{l_1} \\
\therefore & \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\frac{1}{9} \times \frac{3}{1}=\frac{1}{3}
\end{array}\)
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