To demonstrate the large size of the henry unit, a physics professor wants to wi
ID: 1582863 • Letter: T
Question
To demonstrate the large size of the henry unit, a physics professor wants to wind an air-filled solenoid with self-inductance of 1.0 H on the outside of a 13 cm diameter plastic hollow tube using copper wire with a 0.82 mm diameter. The solenoid is to be tightly wound with each turn touching its neighbor (the wire has a thin insulating layer on its surface so the neighboring turns are not in electrical contact).
A)
How long will the plastic tube need to be?
Express your answer to two significant figures and include the appropriate units.
l =
B)
How many kilometers of copper wire will be required?
Express your answer to two significant figures and include the appropriate units.
L =
C)
What will be the resistance of this solenoid?
Express your answer to two significant figures and include the appropriate units.
R =Explanation / Answer
a)We know that the self inductance of the solenoid is given by:
L = u0 N^2 A/l
L = u0 n^2 A l
L = u0 A l/d^2
l = Ld^2/u0 pi r^2
l = 1 x (0.82 x 10^-3)^2/(4 x 3.14 x 10^-7 x 3.14 x 0.065^2) = 40.35 m
Hence, l = 40.35 m
b)We know that
L = pi D l/d
L = 40.35 x 3.14 x 0.13/0.82 x 10^-3 = 20.1 x 10^3 m
Hence, L = 20.1 km
c)We know that
R = rho L/A
R = 1.68 x 10^-8 x 20.1 x 10^3/[3.14 x (0.41 x 10^-3)^2] = 639.75 Ohm
Hence, R = 639.75 Ohm
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