Question

A flat coil of wire having 5 turns has an inductance L The inductance of a similar coil 20 turns is
(correct answer is 16L how?)​

Answer 1

Given:

Flat coil of wire having 5 turns has an inductance of L.

To find:

Inductance of similar coil having 20 turns.

Calculation:

For any coil of wire the inductance is given by the following formula :

$\boxed{ \sf{L = \dfrac{ \mu {N}^{2}A }{l} }}$

$\mu$ refers to the relative permeability of the material. N refers to the number of turns; A refers to the area of the coil and l refers to the length of the coil.

Keeping Material , Area and length constant :

$\boxed{ \sf{L \propto \: {(N)}^{2} }}$

Let new inductance be L2.

$\therefore \: \dfrac{L_{2}}{L_{1}} = \dfrac{ {(N_{2})}^{2} }{{(N_{1})}^{2} }$

$= > \: \dfrac{L_{2}}{L} = \dfrac{ {(20)}^{2} }{{(5)}^{2} }$

$= > \: \dfrac{L_{2}}{L} = \dfrac{ 400 }{25 }$

$= > \: \dfrac{L_{2}}{L} = 16$

$= > L_{2} = 16L$

So final answer is:

$\boxed{ \sf{L_{2} = 16L}}$