A piece of wire is redrawnby pulling it untill it's length is doubled.Compare the new resistance with the original value.
Answers
Answer:The new resistance will be 4 times of the resistance it was before
Explanation:
A piece of wire is redrawn by pulling it until its length is doubled. Compare the new resistance with the
original value.
Given that, length of the wire is doubled.
But, volume of the wire remain in same both cases.
Volume = Area of cross-section x Length
∴ V = A'L' = AL
or
A'
A
=
L
L'
=
L
2L
=
1
2
[∵ L' = 2L]
∴ Ratio of the resistances are,
R'
R
=
ρ
L'
A'
ρ
L
A
=
L'
L
×
A
A'
=
2
1
×
2
1
= 4
i.e., R' = 4R
Thus, the new resistance is four times the original resistance.
A piece of wire is redrawn by pulling it until its length is doubled. Compare the new resistance with the original value.
Volume of the material of wire remains same. So, when length is doubled its area of cross-section will get halfed.
So, if l & a are the original length & area of cross-section of the wire,
0riginal value of Resistance,
R = p × l / a
New value of Resistance,
R' = p × 2l / a/2
= p l/a × 4
= 4R ...