الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

Current & Resistance
Example 7.15
A resistor is constructed by forming a material of resistivity ρ into the
shape of a hollow cylinder of length L and inner and outer radii r a and
r b respectively as shown in figure 7.9. In use, a potential difference is
applied between the ends of the cylinder, producing a current parallel
to the axis. (a) Find a general expression for the resistance of such a
device in terms of L, ρ, r a , and r b . (b) Obtain a numerical value for R
when L=4cm, r a =0.5cm, r b =1.2cm, and ρ=3.5×10 5 Ω.m.
r a
r b
L
Figure 7.9
(a)
(b)
Solution
L ρL
R = ρ =
2
A π ( r b
− r a
2
)
5
ρL
(3.5×
10 )(0.04)
R =
=
= 3.74 × 10
2 2
π ( r b
− r a
) π
2
2
[(0.012)
− (0.005) ]
7
Ω
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