Question

The resistance of a conductor at 30 degree C is 3.25 ohm at 100 degree C is 3.95 ohm .calculate the temperature coefficient of resistance of conductor of its resistance at zero degree C? ​

Answer 1

Answer:

Given: The resistance of a conductor at 20

∘

C is 3.15Ω and at 100

∘

C is 3.75Ω.

To find the temperature co-efficient of resistance of the conductor.

Solution:

Here R 20

=3.15,R 100

=3.75 We know that R t

=R 0

(1+αt)where R 0

= resistance at 0° Cand R t

= resistance at t ∘ C

α= temperature coefficient of resistance

Now,

R 20

=3.15=R 0

(1+20α)....(i)R 100

=3.75=R 0

(1+100α)....(ii)Dividing (i) and (ii), we getR 0

(1+100α)R 0

(1+20α)

= 3.75

3.15

⟹3.75(1+20α)=3.15(1+100α)

⟹3.75+75α=3.15+315α

⟹240α=0.6

⟹α=0.0025 ∘ C −1

From equation(i) ,R 0

= 1+20α3.15

⟹R 0

= 1+20(0.0025)3.15

⟹R 0 =1+0.05

3.15⟹R 0=3Ω

is the temperature co-efficient of resistance of the conductor.

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