Question

The inductance of an air-cored coil is proportional to

1. The square of the number of turns.

2. The square of diameter of the coil

3. A form factor, F dependent on the ratio of coil radius to coil length plus winding depth.

Which of the above statements are correct?
1. 1 and 2 only
2. 1 and 3 only
3. 2 and 3 only
4. 1, 2 and 3

Answer 1

Correct Answer - Option 4 : 1, 2 and 3

The inductance of a coil is given by,

\(L=\frac{{{\mu }_{0}}{{\mu }_{r}}{{N}^{2}}A}{l}=\frac{{{\mu }_{0}}{{\mu }_{r}}{{N}^{2}}\pi r^2}{l}=\frac{{{\mu }_{0}}{{\mu }_{r}}{{N}^{2}}{(\frac{\pi d^2}{4})}}{l}\)

μ0 is the magnetic permeability of free space

μr is the relative permeability

N is number if turns

A is a cross-sectional area

r is the radius of the coil

d is the diameter of the coil

l is length

The inductance is directly proportional to

• The square of the number of turns
• The area i.e. square of the diameter
• The ratio of coil radius to coil length