1) A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4
ID: 1415185 • Letter: 1
Question
1) A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes, respectively (the figure (Figure 1) ). Assume the resistivity is = 3.2×105 m . Determine the resistance for current that passes through the solid in: x, y, z directions.
2)A 14.0-m length of wire consists of 9.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.5 mm . A voltage difference of 75 mV is placed across the composite wire. The resistivity of copper is 1.68×108m and the resistivity of aluminum is 2.65×108m.
a)What is the total resistance (sum) of the two wires?
b)What is the current through the wire?
c)What is the voltage across the copper part?
d)What is the voltage across the aluminum part?
Explanation / Answer
1)
for this we use the formula for the resistance as
R = l / A
(a)
in this part
Rx = Lx /Ayz
= (3.0 x10-5 . m) (1.0 x 10-2 m) / (2.0 x10-2 m) (4.0 x 10-2 m)
= 3.75 x10-4 = 0.375 x10-3
(b)
in this part
Ry = Ly /Axz
= (3.0 x10-5 . m) (2.0 x 10-2 m) / (1.0 x10-2 m) (4.0 x 10-2 m)
= 1.5 x10-3.
(c)
in this part
Rz = Lz /Axy
= (3.0 x10-5 . m) (4.0 x 10-2 m) / (1.0 x10-2 m) (2.0 x 10-2 m)
= 6.0 x10-3
2)
total Resistance = resistance copper + resistance aluminium
(1 l1 + 2 l2)/A
1 (copper)= 1.68×108 1
l1 = 9m
2(Al) = 2.65×108
l2 = 5 m
A = pi * 0.0015^2 /4 = 1.77 * 10^-6 m^2
total resistance = 0.0855 + 0.075 = 0.16 ohm
total current = 0.075 / 0.16 = 0.467 A
total voltage across copper = 0.467 * 0.0855 = 0.04 V
total voltage across aluminium = 0.467 * 0.075 = 0.035 V
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