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Byju's Answer
Standard IX
Physics
Factors That Influence Resistance
If a wire is ...
Question
If a wire is stretched to n times of its original length, its new resistance will be
A
1/n times
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B
n
2
times
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C
n times
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D
None
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Solution
The correct option is
B
n
2
times
Step 1: Volume of the wire
Volume of the wire remains same before and after stretching.
V
i
=
V
f
=
V
Step 2: Resistance of the wire
Initial resistance:
R
=
ρ
l
A
where
A
=
V
/
l
⇒
R
=
ρ
l
2
V
.
.
.
.
(
1
)
Final resistance :
R
′
=
ρ
l
′
2
V
.
.
.
.
(
2
)
Step 3: Dividing equation (2) by (1)
⇒
R
′
R
=
l
′
2
l
2
Given
l
′
=
n
l
⇒
R
′
=
(
n
l
)
2
R
l
2
=
n
2
R
Hence option B is correct.
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