A 61.0 m length of insulated copper wire is wound to form a solenoid of radius 1
ID: 1300707 • Letter: A
Question
A 61.0 m length of insulated copper wire is wound to form a solenoid of radius 1.9 cm. The copper wire has a radius of 0.47 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
a)
Area of Copper Wire
A=pi*r2=pi*(0.47*10-3)2
A=6.94*10-7m2
Resistance of Copper Wore
R=pL/A =(1.68*10-8)*61/(6.94*10-7)
R=1.48 ohms
b)
N=L/2piR =61/2pi*0.019
N=511 turns
c)
Length of resuting solenoid is
L=N*2r =511*2*0.47*10-3
L=0.48 m
d)
Area of solenoid
A=pi*R2=pi*0.0192
A=1.134*10-3m2
self inductance
L=uo*N2*A/l =(4pi*10-7)*5112*1.134*10-3/0.48
L=0.78 mH
e)
equivalent resistacne
Req=0.35+1.48 =1.83 ohms
Time Constant
T=L/R=(0.78*10-3)/1.83
T=4.25*10-4s
T=0.425 ms
f)
Imax=E/Req =6/1.83 =3.28 A
g)
Given
I=0.999Imax
I=Imax[1-e-t/T]
0.999 =1-e-t/4.25*10^-4
ln(0.001)=-t/4.25*10-4
t=2.94 ms
h)
Umas=(1/2)LImax2
Umax=(1/2)*(0.78*10-3)*3.282=4.2 mJ
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.