Question

Flat coil of wire, having 5 turns, has an inductance L. Then the inductance of a similar coil having 20 turns is:

a) 4L
b) L/4
c) 16L
d) L/16
e) L

Answer 1

The inductance of a coil with 20 turns, when the original coil has 5 turns and an inductance L, would be 16 times the original inductance, which is 16L.

Step-by-step explanation:

The inductance L of a coil is dependent on the number of turns N, the cross-sectional area of the coil A, the magnetic permeability of the core material μ, and the length of the coil l. The formula for the self-inductance of a coil is L = k * N^2 * A * μ / l, where k is a constant of proportionality. If the number of turns in a coil is increased from 5 to 20, the inductance increases by a factor of the square of the ratio of the new number of turns to the original number of turns (20/5)^2 = 4^2 = 16. Therefore, if the original inductance is L, the new inductance would be 16L for a coil with 20 turns.