the percentage change in length is 2% and percentage change in radius is 3% of a circular cross
sectional wire then find the percentage change in resistance.
Answers
Answer:
A wire us stretched increase to length by 5% consider to initial length is l and cross sectional area is A
∴ volume V=Al
Now length is increased by 5%
∴ New length =
100
105
=
20
21
l.
If new area is l considering that the volume of the wire is unchanged
V=A l=A;
20
21
l
⇒ A=
21
20
A
Now if resistanty of the wire is ρ then initial Resistance
R
1
=ρ
A
l
Final Resistance
R
2
=ρ
21
20
A
20
21
l
=
A
ρl
(
20
21
)
2
∴
R
1
R
2
=(
20
21
)
2
=
400
441
% change in resistance =(
R
1
R
2
−R
1
)×100%
= 10.25%
Explanation:
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Answer:
A wire is stretched to increase its length by 5%. Calculate percentage change in its resistance.
ANSWER
A wire us stretched increase to length by 5%consider to initial length isl
and cross sectional area isA
∴ volume
V=
Al
Now length is increased by 5%
∴ New length
=
100
105
=
2 0
2 1
l
.
If new area is l considering that the volume of the wire is unchanged
V= A l=
A;
2 0
2 1
l
⇒ A=
2 1
2 0
A
Now if resistanty of the wire is ρ then initial Resistance
R
1
ρ
A
l
Final Resistance
R
2
ρ
21
20
A
20
21
l
=
A
ρl
(
2 0
2 1
)
2
∴
R
1
R
2
=
(
2 0
2 1
)
2
=
400
441
% change in resistance
=
(
R
1
1
R
2
)
×
100%
= 10.25%
Explanation:
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