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  • If the linear dimensions of the core of a cylindrical coil are doubled keeping the number of turns per unit length constant, the inductance of the coil will be (assuming complete winding over the c

If the linear dimensions of the core of a cylindrical coil are doubled keeping the number of turns per unit length constant, the inductance of the coil will be (assuming complete winding over the core)

Option: 1

doubled


Option: 2

four fold


Option: 3

eight times


Option: 4

remains unchanged


Answers (1)

best_answer

The inductance of a coil is given as\mathrm{\mathrm{L}=\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{\ell}} where N = total number of turns of the coil; A = area of cross section of the coil\mathrm{=\pi r^2} ; r = radius of the core of the coil,\mathrm{\ell} = length of the coil. If \mathrm{\ell} is doubled the total number of turns will be doubled

\mathrm{\Rightarrow \frac{L_2}{L_1}=\left(\frac{N_2}{N_1}\right)^2\left(\frac{A_2}{A_1}\right)\left(\frac{\ell_1}{\ell_2}\right)=\left(\frac{N_2}{N_1}\right)^2\left(\frac{\pi r_2^2}{\pi r_1^2}\right)\left(\frac{\ell_1}{\ell_2}\right)=8}

Posted by

Ajit Kumar Dubey

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