Resistivity of a wire of metal A is twice the resistivity of a wire of metal B and the radius of wire of metal A is half the radius of wire of metal B. What should the ratio of the length of wires of metal A and B in order to have the same resistance?
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Answer:
Given,
Two wire A and B,
Diamete of A =d
A
Diameter of B =d
B
d
B
=2×d
A
ρ
B
=2ρ
A
R
A
=
A
A
ρ
A
l
A
=
4
π
d
A
2
ρ
A
l
A
=4×
πd
A
2
ρ
A
l
A
and R
B
=
A
B
ρ
B
l
B
=
4
π
d
B
2
2ρ
A
l
B
=
4
π
(2d
A
)
2
2ρ
A
l
B
=
πd
A
2
2ρ
A
l
B
If both resistances are equal (R
A
=R
B
)
R
A
=R
B
⇒4×
πd
A
2
ρ
A
l
A
=
πd
A
2
2ρ
A
l
B
⇒
l
B
l
A
=
2
1
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