A wire of cross-sectional are d A, length L1, resistivity ρ1 and temperature coefficient of resistivity α1 is connected in series to a second wire of length L2, resistivity ρ2, temperature coefficient of resistivity α2 and the same area A, so that wires carry same current. Total resistance R isindependent of temperature for small temperature change if (Thermal expansion effect is negligible)
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a
α1 =−α2
b
ρ1L1α1+ρ2L2α2=0
c
L1α1+L2α2=0
d
None
answer is B.
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Detailed Solution
Let initial resistances of the wires are R1 and R2 respectively. Then R'1 +R'2=R1+R2⇒R11+α1ΔT +R21+α2ΔT=R1+R2⇒R1 α1+R2α2=0⇒ ρ1L1A α1+ρ2L2Aα2=0ρ1L1α1+ρ2L2α2=0