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  • Two solenoids of equal number of turns have their lengths and the radii in the same ratio 1 : 2. The ratio of their self inductances will be:Option: 1 <

Two solenoids of equal number of turns have their lengths and the radii in the same ratio 1 : 2. The ratio of their self inductances will be:

Option: 1

1:2


Option: 2

2:1


Option: 3

1:1


Option: 4

1:4


Answers (1)

best_answer

Self inductance of a solenoids, \mathrm{\mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{l}=\frac{\mu_0 \mathrm{~N}^2 \pi \mathrm{r}^2}{l}}

Where I is the length of the solenoids, N is the total number of turns othe solenoid and A is the area of crosssection of the solenoid.

\mathrm{ \therefore \quad \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\left(\frac{\mathrm{N}_1}{\mathrm{~N}_2}\right)^2\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2\left(\frac{l_2}{l_1}\right) }

\mathrm{ Here, \mathrm{N}=\mathrm{N}_2, \frac{l_1}{l_2}=\frac{1}{2}, \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{1}{2}}

\mathrm{\therefore \quad \frac{L_1}{L_2}=\left(\frac{1}{2}\right)^2\left(\frac{2}{1}\right)=\frac{1}{2}}

 

Posted by

HARSH KANKARIA

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