Question

Estimate the inductance L of a coil that is 12 cm long, made of about 235 copper-wire turns and a diameter of about 1.7 cm. Show work and units. Compare your answer to the nominal value here 78+- 22mH

Answer 1

Inductance as calculated is 13.12 mH

Solution:

As per the question:

Length of the coil, l = 12 cm = 0.12 m

Diameter, d = 1.7 cm = 0.017 m

No. of turns, N = 235

Now,

Area of cross-section of the wire, A =
`(\pi d^(2))/(4) = (\pi * 0.017^(2))/(4) = 2.269* 10^(- 4)\ m^(2)`

We know that the inductance of the coil is given by the formula:

`L = (mu_(o)AN^(2))/(l) = (4\pi * 10^(- 7)* 2.269* 10^(- 4)* 235^(2))/(0.12) = 1.312* 10^(- 4)\ H = 13.12\ mH`