CHAPTER 3 RESISTANCE VARIATION
EXERCISE 11, Page 24
1. The resistance of a 2 m length of cable is 2.5 . Determine (a) the resistance of a 7 m length of
the same cable and (b) the length of the same wire when the resistance is 6.25 .
(a) If the resistance of a 2 m length of cable is 2.5 , then a 1 m length of cable is 1.25 
Thus, the resistance of a 7 m length of cable is 7  1.25 = 8.75 
(b) If the resistance of a 2 m length of cable is 2.5 , then a
2
m length of cable is 1 
2.5
Thus, a resistance of 6.25  corresponds to a length of 6.25 
2
m=5m
2.5
2. Some wire of cross-sectional area 1 mm 2 has a resistance of 20 . Determine (a) the resistance
of a wire of the same length and material if the cross-sectional area is 4 mm 2 , and (b) the crosssectional area of a wire of the same length and material if the resistance is 32 .
(a) R 
1
20
thus a wire of cross-sectional area 4 mm 2 has a resistance of
=5
a
4
(b) Since wire of cross-sectional area 1 mm 2 has a resistance of 20 ,
then a c.s.a. of 20 mm 2 has a resistance of 1 .
Hence, a resistance of 32  corresponds to a c.s.a. of
20
= 0.625 mm2
32
3. Some wire of length 5 m and cross-sectional area 2 mm 2 has a resistance of 0.08 . If the wire is
drawn out until its cross-sectional area is 1 mm 2 , determine the resistance of the wire.
R
l
 (5)
i.e. 0.08 
a
2 106
from which, resistivity,  
0.08  2 106
 0.032 106
5
If c.s.a. = 1 mm 2 (i.e. half the original c.s.a.) then the length will double, i.e. l = 2  5 = 10 m
 l  0.032 10  10 

Hence, resistance, R 
= 0.32 
a
1106
6
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4. Find the resistance of 800 m of copper cable of cross-sectional area 20 mm2. Take the resistivity of
copper as 0.02 μm
6
 l  0.02 10 m   800 m 

Resistance, R 
= 0.8 
a
20 106 m 2
5. Calculate the cross-sectional area, in mm 2 , of a piece of aluminium wire 100 m long and having
a resistance of 2 . Take the resistivity of aluminium as 0.03 106 m
6
l
 l  0.03 10 m  100 m 
Since R 
then c.s.a., a =

 1.5 106 m 2 = 1.5 mm2
a
R
2
6. The resistance of 500 m of wire of cross-sectional area 2.6 mm2 is 5 . Determine the resistivity of the
wire in μm
Since resistance, R 
l
then
a
6
2
R a  5    2.6 10 m 
resistivity, ρ =

 26 109 m  0.026 106 m = 0.026 μm
l
500 m
7. Find the resistance of 1 km of copper cable having a diameter of 10 mm if the resistivity of
copper is 0.017 106 m .
6
3
 l  l  0.017 10 m 110 m 


Resistance, R 
= 0.216 
2
a  r2
  5 106 m 2
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EXERCISE 12, Page 26
1. A coil of aluminium wire has a resistance of 50  when its temperature is 0oC. Determine its
resistance at 100oC if the temperature coefficient of resistance of aluminium at 0oC is 0.0038/oC
Resistance R  = R0(1 + α0 )
Hence, resistance at 100oC, R100 = 50[1 + (0.0038)(100)]
= 50[1 + 0.38] = 50(1.38) = 69 
2. A copper cable has a resistance of 30  at a temperature of 50C. Determine its resistance at
0C. Take the temperature coefficient of resistance of copper at 0C as 0.0043/C.
R 50  R 0 1  0 (50) from which,
resistance at 0C, R 0 
R 50
30
30


= 24.69 
1  50  0 1  50(0.0043) 1.215
3. The temperature coefficient of resistance for carbon at 0C is -0.00048/C. What is the
significance of the minus sign? A carbon resistor has a resistance of 500  at 0C. Determine its
resistance at 50C.
For carbon, resistance falls with increase of temperature, hence the minus sign.
R 50  R 0 1  0 (50)  500 1  50(0.00048)   500 1  0.024 = 488 
4. A coil of copper wire has a resistance of 20  at 18oC. If the temperature coefficient of resistance of
copper at 18oC is 0.004/oC, determine the resistance of the coil when the temperature rises to 98oC
Resistance at oC,
R  = R18 [1 + α20( - 18)]
Hence, resistance at 98oC, R98 = 20 [1 + (0.004)(98 - 18)]
= 20 [1 + (0.004)(80)]
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= 20 [1 + 0.32] = 20(1.32) = 26.4 
5. The resistance of a coil of nickel wire at 20C is 100 . The temperature of the wire is increased
and the resistance rises to 130 . If the temperature coefficient of resistance of nickel is
0.006/C at 20C, determine the temperature to which the coil has risen.
R   R 20 1  20 (  20)
130  100 1  0.006    20    100  0.6    20 
i.e.
i.e. 130 – 100 = 0.6 ( - 20)
and
( - 20) =
130  100 30

 50
0.6
0.6
Hence, temperature to which the coil has risen,  = 50 + 20 = 70C
6. Some aluminium wire has a resistance of 50  at 20oC. The wire is heated to a temperature of 100oC.
Determine the resistance of the wire at 100oC, assuming that the temperature coefficient of
resistance at 0oC is 0.004/oC
R20 = 200  , α0 = 0.004/oC and
Hence, R100 =
R 20
[1   0 (20)]

R100 [1   0 (100)]
50[1 100(0.004)]
50[1  0.4]
R 20 [1  100 0 ]
50(1.4)
=
=
=
= 64.8 
[1  20  0 ]
[1  20(0.004)]
[1  0.08]
(1.08)
i.e. the resistance of the wire at 100oC is 64.8 , correct to 3 significant figures.
7. A copper cable is 1.2 km long and has a cross-sectional area of 5 mm 2 . Find its resistance at
80C if at 20C the resistivity of copper is 0.02 106 m and its temperature coefficient of
resistance is 0.004/C.
6
3
 l  0.02 10 m 1.2 10 m 
Resistance at 20C, R 20  
= 4.8 
a
5 106 m 2
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Resistance at 80C, R 80  R 20 1   20 (80  20)   4.8 1  0.004  60    4.8 1.24 = 5.95 
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EXERCISE 13, Page 28
1. Determine the value and tolerance of a resistor having a colour coding of: blue-grey-orange-red
blue-grey-orange-red corresponds to: 68  103 2% from Table 3.1, page 26 of textbook
68 k 2%
i.e.
2. Determine the value and tolerance of a resistor having a colour coding of:
yellow-violet-gold
yellow-violet-gold corresponds to: 47  101 20% from Table 3.1, page 26 of textbook
4.7  20%
i.e.
3. Determine the value and tolerance of a resistor having a colour coding of:
blue-white-black-black-gold
blue-white-black-black-gold corresponds to: 690  1 5% from Table 3.1, page 26 of textbook
690  5%
i.e.
4. Determine the colour coding for a 51 k four-band resistor having a tolerance of 2%
51 k 2% = 51  103 2% which corresponds to a colour coding (from Table 3.1, page 26 of
textbook) of:
green-brown-orange-red
5. Determine the colour coding for a 1 M four-band resistor having a tolerance of 10%
1 M 10% = 106 2% = 10  105 10% which corresponds to a colour coding (from Table 3.1,
page 26 of textbook) of:
brown-black-green-silver
6. Determine the range of values expected for a resistor with colour coding:
red-black-green-silver
red-black-green-silver corresponds to: 20  105 10% from Table 3.1, page 26 of textbook
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2 M 10%
i.e.
10% of 2 M =
10
 2 = 0.2 M
100
Thus, the range of values is from 2 – 0.2 to 2 + 0.2
i.e.
1.8 M to 2.2 M
7. Determine the range of values expected for a resistor with colour coding:
yellow-black-orange-brown
yellow-black-orange-brown corresponds to: 40  103 1% from Table 3.1, page 26 of textbook
40 k 1%
i.e.
1% of 40 k =
1
 40000 = 400 
100
Thus, the range of values is from 40000 – 400 to 40000 + 400
i.e.
39600  to 40400 
or
39.6 k to 40.4 k
8. Determine the value of a resistor marked as (a) R22G (b) 4K7F
(a) R22G = 0.22   2% from Table 3.2, page 27 of textbook
(b) 4K7F = 4.7 k  1% from Table 3.2, page 27 of textbook
9. Determine the letter and digit code for a resistor having a value of 100 k 20%
100 k 20% corresponds in letter and digit form to: 100KJ from page 27 of textbook
10. Determine the letter and digit code for a resistor having a value of 6.8 M  20%
6.8 M  20% corresponds in letter and digit form to: 6M8M from page 27 of textbook
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