A wire of resistance 10 ohm is stretched to double its length. Calculate its new resistance and resistivity.
Answers
When wire is doubled over itself, area is doubled and length is halved.
Resistance is proportional to Length and inversaly proportional to Area.
So
R` = R(1/2)/2
R'=R/4
R' = 10/4 =2.5 Ohm
Resistivity doesn't depend on shape of conductor
Answer:
In the given question, we are asked to calculate the resistance of the wire if it's length is doubled. Let us proceed towards the question.
Explanation:
Given: Resistance of the wire = 10Ω
To Find: New resistance as well as resistivity after the length is doubled.
Now, we know a property of a material by nature, and it is that no matter in which shape or size we transform a given substances, if the original dimensions aren't disturbed, then the volume of the substances before and after changing it's form, still remains same.
Hence, even if we double the length of the wire, if the area wasn't disturbed at all, then volume would be same. Hence, to keep the volume constant, the area must be reduced to half.
Therefore, new length (L') and area (A') of wire would be:
⇒ L' = 2L and A' = A/2
now, we know,
Resistance(R) of a wire = ρL/A ( eq. 1 )
where, ρ = Resistivity of wire. It's a constant.
Putting L=2L and A=A/2, we get new resistance R' as:
R' = ρ(2L)/(A/2)
= 4(ρL/A)
R' = 4R
Hence, new resistance will be 4 times the old resistance.
The old resistance = 10Ω
Hence, new resistance = 4×10 = 40Ω.
Resistivity(ρ) = RA/L
ρ = 10×(A/L) Ω - m
Knowing the length and area, we can calculate the resistivity.