Calculate the ratio of the resistivity of 2 wires having the same length and same resistance with area of cross section 2sq.m and 5 sq.m respectively.
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PHYSICS
Two wires A and B, having resistivity ρ
A
=3×10
−5
Ωm and ρ
a
=6×10
−5
Ωm of same cross section area are pointed together to form a single wire. If the resistance of the joined wire does not change with temperature, then find the ratio of their lengths given that temperature coefficient of resistivity of wires A and B are α
A
=4×10
−5
/
∘
C and α
B
=−4×10
−6
/
∘
C. Assume that mechanical dimensions do not change with temperature.
December 26, 2019avatar
Shweta Gogawale
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ANSWER
we know that , ρ=ρ
0
(1+αΔT) and R=
A
ρl
and when rods are combined end to end it behaves as series combination
so, combined resistance will be : R=R
1
+R
2
this gives , R=
A
ρ
1
l
1
+
A
ρ
2
l
2
using equation of roh, we get : R=
A
1
(ρ
1
l
1
(1+α
1
ΔT)+ρ
2
l
2
(1+α
2
ΔT))
=
A
1
(ρ
1
l
1
+ρ
2
l
2
+(ρ
1
l
1
α
1
+ρ
2
l
2
α
2
)ΔT)
Given that this resistance does not depend on temperature therefore coefficient of temperature difference will be zero , i.e,
ρ
1
l
1
α
1
+ρ
2
l
2
α
2
=0
This gives :
l
2
l
1
=
ρ
1
α
1
−ρ
2
α
2
=
3×10
−5
×4×10
−5
6×10
−5
×4×10
−6
=0.2
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