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Question
Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of copper is 1.7 × 10−8 Ω m.
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Solution
Length of the cable wire, l = 1 km = 1000 m
Diameter of the cable wire, d = 0.5 mm
Area of cross-section,
A `= "A"pi^2`
`= 3.14xx(2.5xx10^-4)^2`
`= 0.96xx10^(-8)m^2`
To find the resistance of the copper cable,
We know that `"R"="l"/"A"`
R `= (1.7xx10^-8xx1000)/(19.6xx10^-8)`
So, R = 86.73 Ω
Thus, the resistance of the copper wire, R = 86.73 Ω
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| Electrical resistivity of some substances at 20°C | ||
| − | Material | Resistivity (Ω m) |
| Conductors |
Silver | 1.60 × 10−8 |
| Copper | 1.62 × 10−8 | |
| Aluminium | 2.63 × 10−8 | |
| Tungsten | 5.20 × 10−8 | |
| Nickel | 6.84 × 10−8 | |
| Iron | 10.0 × 10−8 | |
| Chromium | 12.9 × 10−8 | |
| Mercury | 94.0 × 10−8 | |
| Manganese | 1.84 × 10−6 | |
| Alloys |
Constantan (alloy of Cu and Ni) |
49 × 10−6 |
| Manganin (alloy of Cu, Mn and Ni) |
44 × 10−6 | |
| Nichrome (alloy of Ni, Cr, Mn and Fe) |
100 × 10−6 | |
| Insulators | Glass | 1010 − 1014 |
| Hard rubber | 1013 − 1016 | |
| Ebonite | 1015 − 1017 | |
| Diamond | 1012 − 1013 | |
| Paper (dry) | 1012 | |
How will the resistance of a wire be affected if its
- length is doubled, and
- radius is also doubled ?
Give justification for your answer.
