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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
On what factors does the resistance of a conductor depend?
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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 | |
List the factors on which the resistance of a conductor in the shape of a wire depends.
Distinguish between good conductors, resistors and insulators. Name two good conductors, two resistance and two insulators.
What happens to the resistance as the conductor is made thicker?
What do you understand by the "resistivity" of a substance?
How does the resistance of a conductor depend on:
area of cross-section of the conductor?
What would be the effect on the resistance of a metal wire of:
increasing its diameter?
How will you infer with the help of an experiment that the same current flows through every part of the circuit containing three resistors R1, R2 and R3 in series connected to a battery of V volts?
Assertion: Conductors allow the current to flow through themselves.
Reason: They have free charge carriers.
