Q. 81

Expert-verifiedFound in: Page 875

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

81. III In recent years it has been possible to buy a capacitor. This is an enormously large amount of capacitance. Suppose you want to build a oscillator with a capacitor. You have a spool of 0.25-mm-diameter wire and a -diameter plastic cylinder. How long must your inductor be if you wrap it with 2 layers of closely spaced turns?

The length of the inductor is

The expression of the resonant frequency is as follows:

Here, L and C are the inductance and capacitance of the circuit.

After rearranging and substituting values

Therefore, the inductance of the inductor is .

There are two layers of wires so that the number of turns gets doubled. Hence, the total number of turns in the inductor of two layers is as follows:

Here, d is the diameter of the wire and N is the number of turns.

The area of the cross-section of the plastic cylinder is as follows:

Here, is the diameter of the plastic cylinder.

The expression of the inductance is as follows:

Here, is the number of turns, is the area of cross-section, is the length of the inductor, and is the permeability of free space.

After rearranging the above equation, the length of the inductor as follows:

Therefore, the length of the inductor is

94% of StudySmarter users get better grades.

Sign up for free