MHT CET · Physics · Electromagnetic Induction
If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will
- A remain constant
- B be halved
- C become 9 times
- D become \(\frac{1}{9}\) times
Answer & Solution
Correct Answer
(C) become 9 times
Step-by-step Solution
Detailed explanation
Self-inductance of a solenoid is given by
\(\begin{aligned}
& \quad \mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{l} \\
& \therefore \quad \mathrm{~L} \propto \mathrm{~N}^2 \\
& \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\left(\frac{\mathrm{N}_1}{\mathrm{~N}_2}\right)^2 \\
& \frac{\mathrm{~L}}{\mathrm{~L}_2}=\left(\frac{\mathrm{N}}{3 \mathrm{~N}}\right)^2 \\
& \mathrm{~L}_2=9 \mathrm{~L}
\end{aligned}\)
\(\begin{aligned}
& \quad \mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{l} \\
& \therefore \quad \mathrm{~L} \propto \mathrm{~N}^2 \\
& \frac{\mathrm{~L}_1}{\mathrm{~L}_2}=\left(\frac{\mathrm{N}_1}{\mathrm{~N}_2}\right)^2 \\
& \frac{\mathrm{~L}}{\mathrm{~L}_2}=\left(\frac{\mathrm{N}}{3 \mathrm{~N}}\right)^2 \\
& \mathrm{~L}_2=9 \mathrm{~L}
\end{aligned}\)
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