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Question
The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the wire is 50 × 10-8 Ω, find the length of this wire.
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Solution
Given, Radius, r = 0.01 cm = 0.0001 m
Resistance, R = 10 Ω
Resistivity, `rho = 50 xx 10^-8` Ω m
R = `rho "L"/"A"`
L = `"RA"/rho`
`= (10 xx 3.14 xx (0.0001)^2)/(50 xx 10^-8)`
= 0.628 m
Hence, the length of the wire is 0.628 m.
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RELATED QUESTIONS
Use the data in the Table given below to answer the following –
Which among iron and mercury is a better conductor?
Table give below Electrical resistivity of some substances at 20°C
| 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 | |
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