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Question

The resistance of a conductor is 5 ohm at 50C and 6 ohm at 100C. Its resistance at 0C is

A
3 ohm
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B
4 ohm
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C
1 ohm
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D
2 ohm
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Solution

The correct option is B 4 ohm
We know that RT=Ro(1+αT) where RT= resistance at temp T,
Ro= resistance at 0C
α= temperature coefficient of resistance.
5=Ro[1+50 α].....(1)
and
6=Ro[1+100 α].....(2)
Dividing (1) by (2),
56=1+50 α1+100 α
6+300 α=5+500 α
or 1=200 α
or α=1200
From Eq. (1),
5=Ro[1+50×1200]
or 5=Ro[1+14]
or Ro=5×45 Ω=4 Ohm

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