Misr University for Science and Technology

College of Engineering science and Technology

Solution of Sheet 7
1- During the 4.0 min a 5.0 A current College
Information Technology is set up in a wire, how many (a) coulombs and (b)
electrons pass through any cross section across the wire’s width?
(a) The charge that passes through any cross section is the product of the current and time.
Since t = 4.0 min = (4.0 min)(60 s/min) = 240 s,
q = It = (5.0 A)(240 s) = 1.2× 103 C.
(b) The number of electrons N is given by q = Ne, where e is the magnitude of the charge
on an electron. Thus,
N = q/e = (1200 C)/(1.60 × 10–19 C) = 7.5 × 1021.
2- A small but measurable current of 1.2 × 10-10A exists in a copper wire whose diameter
is 2.5 mm. The number of charge carriers per unit volume is 8.49×1028 m-3. Assuming the
current is uniform; calculate the (a) current density and (b) electron drift speed.
(a) The magnitude of the current density vector is

(b) The drift speed of the current-carrying electrons is

3- How long does it take electrons to get from a car battery to the starting motor? Assume
the current is 300 A and the electrons travel through a copper wire with cross-sectional
area 0.21 cm2 and length 0.85 m. The number of charge carriers per unit volume is
8.49×1028 m-3.
We use vd = J/ne = i/Ane. Thus,

4- Calculate the resistance of an aluminum cylinder that has a length of 10 cm and a cross-
sectional area of 2×10-4 m2. Repeat the calculation for a cylinder of the same dimensions
and made of glass having a resistivity of 3.0 × 1010 Ωm.
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 Misr University for Science and Technology
College of Engineering science and Technology

Similarly, for glass we find that

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5- (a) Calculate the resistance per unit length of a 22-gauge nichrome wire of radius
0.321 mm. (b) If a potential difference of 10.0 V is maintained across a 1.00 m length of
the nichrome wire, what is the current in the wire? (c) The wire is melted down and recast
with twice its original length. Find the new resistance RN as a multiple of the old
resistance R0.
A = pr2 = p (0.321 × 10-3 m)2 = 3.24 × 10-7 m2
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(c)
VN = VO → ANlN = AOlO → AN = AO(lO/lN)
AN = AO(l O/2lO) = AO/2
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#! "# ! & #$ #!
6- A resistance thermometer, which measures temperature by measuring the change in
resistance of a conductor, is made of platinum and has a resistance of 50.0Ω at 20.0°C.
(a) When the device is immersed in a vessel containing melting indium, its resistance
increases to 76.8 Ω. From this information, find the melting point of indium. (b) The
indium is heated further until it reaches a temperature of 235°C. What is the ratio of the
new current in the platinum to the current Imp at the melting point?
Solution
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College of Engineering science and Technology

$%!&" ! '"!""
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" !!() # #"!! " "# # !# #" '"!"" #
= #!$ "#

Substitute T0 = 20.0°C and obtain the melting point of indium:

T = 157°C
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Substitute T = 235°C, T mp = 157°C, and the value for a, obtaining the desired ratio:
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7. How much energy is dissipated as heat during a two-minute time interval by a 1.5-kW
resistor which has a constant 20-V potential difference across its leads?
a. 58 J
b. 46 J
c. 32 J
d. 72 J
e. 16 J
ANS: C
8. A 4.0-W resistor has a current of 3.0 A in it for 5.0 min. How many electrons pass
through the resistor during this time interval?
a. 7.5 ´ 1021
b. 5.6 ´ 1021
c. 6.6 ´ 1021
d. 8.4 ´ 1021
e. 2.1 ´ 1021
ANS: B
9. If 5.0 ´ 10 electrons pass through a 20-W resistor in 10 min, what is the potential
21

difference across the resistor?

a. 21 V
b. 32 V
c. 27 V
d. 37 V
e. 54 V
 Misr University for Science and Technology
College of Engineering science and Technology

ANS: Information
C Technology College
10. How many electrons pass through a 20-W resistor in 10 min if there is a potential
drop of 30 volts across it?
a. 5.6 ´ 1021
b. 7.5 ´ 1021
c. 9.4 ´ 1021
d. 1.1 ´ 1021
e. 3.8 ´ 1021
ANS: A
11. A wire (length = 2.0 m, diameter = 1.0 mm) has a resistance of 0.45W. What is the
resistivity of the material used to make the wire?
a. 5.6 ´ 10-7 W × m
b. 1.2 ´ 10-7 W × m
c. 1.8 ´ 10-7 W × m
d. 2.3 ´ 10-7 W × m
e. 7.1 ´ 10-7 W × m
ANS: C
12. A small bulb is rated at 7.50 W when operated at 125 V. The tungsten filament has a
temperature coefficient of resistivity a = 4.50 ´ 10-3 / °C. When the filament is hot and
glowing, its temperature is seven times room temperature (20 °C). What is the
resistance of the filament (in ohms) at room temperature?
a. 234
b. 1 350
c. 2 080
d. 4 530
e. 5 630
ANS:A
13. A nichrome wire and an aluminum wire, each with the same initial resistance, have
the same change in resistance when heated separately. (rAl = 2.82 ´ 10-8 W × m; aAl =
3.9 ´ 10-3 / °C; rnichrome = 1.50 ´ 10-6 W × m; anichrome = 0.40 ´ 10-3 / °C.) The ratio of
the temperature change of the nichrome wire to the temperature change of the
aluminum wire is
a. 0.019.
b. 0.10.
c. 0.18.
d. 9.8.
e. 53.
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College of Engineering science and Technology

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