A 58.0 m length of insulated copper wire is wound to form a solenoid of radius 1

Question

A 58.0 m length of insulated copper wire is wound to form a solenoid of radius 1.8 cm. The copper wire has a radius of 0.51 mm. (a) What is the resistance of the wire? ? (b) Treating each turn of the solenoid as a circle, how many turns can be made with the wire? turns (c) How long is the resulting solenoid? m (d) What is the self-inductance of the solenoid? mH (e) If the solenoid is attached to a battery with an emf of 6.0 V and internal resistance of 350 m?, compute the time constant of the circuit. ms (f) What is the maximum current attained? A (g) How long would it take to reach 99.9% of its maximum current? ms (h) What maximum energy is stored in the inductor? mJ

Explanation / Answer

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Too many

A 57.0 m length of insulated copper wire is wound to form a solenoid of radius 2.2 cm. The copper wire has a radius of 0.53 mm.
(a) What is the resistance of the wire?
Resistance of a wire in
R = L/A
is resistivity of the material
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2 (n-m)

A = r² = (0.00051)²
R = L/A
R = (17.2e-9)(58)/(0.00051)²


(b) Treating each turn of the solenoid as a circle, how many turns can be made with the wire?
circumference = 2(0.00051)
divide 58 by the circumference to get number of turns

(c) How long is the resulting solenoid?

number of turns x diameter 2(0.00051) Too many

A 57.0 m length of insulated copper wire is wound to form a solenoid of radius 2.2 cm. The copper wire has a radius of 0.53 mm.
(a) What is the resistance of the wire?
Resistance of a wire in
R = L/A
is resistivity of the material
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2 (n-m)

A = r² = (0.00051)²
R = L/A
R = (17.2e-9)(58)/(0.00051)²


(b) Treating each turn of the solenoid as a circle, how many turns can be made with the wire?
circumference = 2(0.00051)
divide 58 by the circumference to get number of turns

(c) How long is the resulting solenoid?

number of turns x diameter 2(0.00051) Too many

A 57.0 m length of insulated copper wire is wound to form a solenoid of radius 2.2 cm. The copper wire has a radius of 0.53 mm.
(a) What is the resistance of the wire?
Resistance of a wire in
R = L/A
is resistivity of the material
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2 (n-m)

A = r² = (0.00051)²
R = L/A
R = (17.2e-9)(58)/(0.00051)²


(b) Treating each turn of the solenoid as a circle, how many turns can be made with the wire?
circumference = 2(0.00051)
divide 58 by the circumference to get number of turns

(c) How long is the resulting solenoid?

number of turns x diameter 2(0.00051)

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