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प्रश्न
How will the resistance of a wire be affected if its
- length is doubled, and
- radius is also doubled ?
Give justification for your answer.
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उत्तर
R `=(rho"l")/"A"`
Where, `rho` = electrical resistivity
l = length of the conductor
A = cross-sectional area of the conductor
Hence if the length is double then
⇒ `"R"_1=rho((2"l"))/"A"`
`therefore "R"_1 = 2("R")`
So, if the length of the resistance gets doubled then resistance also gets doubled.
Now when the radius is double then
⇒ `"R"_2 = (rho"l")/"A"`
⇒`"R"_2 = (rhol)/(pi(2"r")^2`
`therefore "R"_2 = 1/4("R")`
So if the radius gets doubled then resistance will be `(1/4)^"th"` of initial resistance.
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संबंधित प्रश्न
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 | |
Why are copper and aluminium wires usually employed for electricity transmission?
Why are alloys commonly used in electrical heating devices? Give reason.
Fill in the following blanks with suitable words:
Copper is a good .......... Plastic is an ..........
Which has more resistance:
a long piece of nichrome wire or a short one?
Give two examples of substances which are good conductors of electricity. Why do you think they are good conductors of electricity?
What would be the effect on the resistance of a metal wire of:
increasing its length?
What would be the effect on the resistance of a metal wire of:
increasing its diameter?
How does the resistance of a wire change when:
its material is changed to one whose resistivity is three times?
Calculate the area of cross-section of a wire if its length is 1.0 m, its resistance is 23 Ω and the resistivity of the material of the wire is 1.84 × 10−6 Ω m.
