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Question

The resistance of wire at 20C is 20Ω, and at 300C resistance of wire is 50Ω. The temperature at which its resistance will be 40Ω is

A
100C
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B
107C
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C
207C
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D
200C
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Solution

The correct option is C 207C
R=R0{1+αΔθ}
So,
20=R0{1+α.20}
50=R0{1+α.300}
25=1+20α1+300α2+600α=5+100α
500α=3
α=6×103
Hence,
R=R0{1+αΔθ}
50=R0{1+6×103×300}
=R0=502.8

R=502.8{1+6×103×Δθ}
40=502.8{1+6×103×Δθ}
Δθ=206.670C which is close to 2070C.

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