Problem 30.81 Part A In recent years it has been possible to buy a 1.0 F capacit

Question

Problem 30.81 Part A In recent years it has been possible to buy a 1.0 F capacitor This is an enormously large amount of capacitance. Suppose you want to build a 3.2 Hz oscillator with a 1.0 F capacitor. You have a spool of 0.30-mm-diameter wire and a 3.4-cm-diameter plastic cylinder How long must your inductor be if you wrap it with 2 layers of closely spaced turns? Express your answer to two significant figures and include the appropriate units. Submit My Answers Give Up Incorrect; Try Again; 2 attempts remaining

Explanation / Answer

Determine the inductance that resonates with 1F at a frequency of 3.2Hz using:

f = 1/(2*pi*sqrt(LC)) ======> L = 2.5 mH

Now determine how large the solenoid is for that inductance.
The second link gives a formula for multilayer air cored solenoid inductors as:

L = (31.6 * r1^2 * n^2) / (6 * r1 + 9 * l + 10 * ( r2 - r1))
Where:
L = inductance in micro henry = 2.5 mH
r1 = inside coil radius in meters = 1.5*10^-4 m
r2 = outside coil radius in meters = 0.017 m
l = coil length in meters = ?
n = # of turns total = 113.3

The third link is a calculator using a similar formula. It looks like 113.3 turns on 3.4 cm diameter in two layers and 6.8 cm long. The wire is 0.03 cm diameter.

2.5*10^-3 = 0.00912702879/(9*l + 0.1694)

l = 0.3868 m = 38.68 cm

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