A wire of 10-ohm resistance stretched to thrice its original length. What will be its 1) new resistivity 2) new resistance

Resistance is the property of the material that restricts the flow of electrons. There are four factors affecting resistance which are Temperature, Length of wire, Area of the cross-section of the wire, and nature of the material.

Factors that affect resistance

The resistance of a wire depends both on the cross-sectional area and length of the wire and on the nature of the material of the wire. Thick wires have less resistance than thin wires. Longer wires have more resistance than short wires. Copper wire has less resistance to thin steel wire of the same size. Electrical resistance also depends on temperature. At a certain temperature and for a particular substance.

  • material, eg copper, has lower resistance than steel
  • length – longer wires have greater resistance
  • thickness – smaller diameter wires have greater resistance
  • temperature – heating a wire increases its resistance

Solution

(i) Since resistivity depends on the nature of the material of wire and is independent of dimensions of wire, so the resistivity remains unchanged.

The resistance of the wire is directly proportional to its length and inversely proportional to its cross-sectional area. So,
∴R=ρlA
Where,

l – length of the wire,

A – cross-sectional area of the wire
ρ – resistivity of the wire (proportional constant)
Resistivity is the property of the material and the length does not play a vital role in changing the resistivity.
(ii) In both cases, the volume of the wire is the same.

V = Al

R = ρl/A

R’ = 9ρl/A = 9R

R’ = 9*10= 90Ω

Check out the video below to know more about the factors that affect resistance

Further Reading

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