Question

You have a 100-m copper wire with cross-sectional area 0.25 mm2 and resistivity 1.7×10−8Ω⋅m. You make a 780-turn solenoid by winding the wire on a plastic tube (diameter 4.0 cm, length 10 cm).

a)

Determine the resistance of the solenoid.

Express your answer with the appropriate units.

b)

Determine the inductance of the solenoid.

Express your answer with the appropriate units.

c)

Determine the frequency of the alternating current at which the inductive reactance of the solenoid is equal to its resistance.

Express your answer with the appropriate units.

Answer 1

a)

R = rho * L / A

R = 1.7*10^-8* 100 / (0.25*10^-6)

R = 6.8 ohm

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b)

L = uo N^2 A /l

L = 4* 3.14*10^-7* 780^2* 3.14/4* 0.04^2 / 0.1

L = 9.6*10^-3 H

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c)

R = wL

w = R/L

2* 3.14* f = 6.8 / (9.6*10^-3)

f = 112.82 Hz

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