A 63.0 m length of insulated copper wire is wound to form a solenoid of radius 2
ID: 1422563 • Letter: A
Question
A 63.0 m length of insulated copper wire is wound to form a solenoid of radius 2.3 cm. The copper wire has a radius of 0.53 mm. (Assume the resistivity of copper is
= 1.7 108 · m.)
(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
(a)
R = L/A
R = (1.7 * 10^-8 * 63.0)/(3.14*(0.53*10^-3)^2)
R = 1.214
(b)
No of turns, = 63.0 / (2*3.14 * 0.023)
N = 436 TURNS
(c)
Length of the solenoid,
L = 2 * r * N
L = 2* 0.53*10^-3 * 436 m
L = 0.462 m
(d)
I = oN²A/L
l = (4*PI*10^-7 *436^2 *(3.14*(0.53*10^-3)^2)) / 0.462
I = 4.56 * 10^-7 H
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