Question

The resistance of a wire is 5ohmat50∘C and 6ohmat100∘C. The resistance of the wire at 0∘C will be

Answer 1

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Answer:

Its resistance at 0∘C is 4 ohm.

Explanation:

RT=(1+αT)R, where

RT=Resistance at any temperature,
α=constant of material,
R=resistance at Zero degree Celsius.

At 50 degrees Celsius:

R50=(1+50α)R=5 ohm  (1)

At 100 degrees Celsius:

R100=(1+100α)R=6 ohm  (2)

At zero degrees Celsius:

R0=(1+0)R
R0=R  (3)

Determination R from equations (1) and (2)** by

(1)(2)⇒1+50α1+100α=56

6+300α=5+500α⇒α=1200

Use this value in equation (1)

(1+1200⋅50)⋅R=5⇒54⋅R=5⇒R=4 ohm

According to equation (3), you have

R0=R=4 ohm

Therefore, its resistance at 0∘C is 4 ohm.

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