Question

(b) The resistance of a conductor is X Ohm at ℃ temperature. Find the

temperature at which the resistance of conductor becomes 3X Ohm. The

temperature coefficient of resistance for conductor is . × ି

℃ି​

Answer 1

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

∘

C

and 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 get

R

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+20α

3.15

⟹R

0

=

1+20(0.0025)

3.15

⟹R

0

=

1+0.05

3.15

⟹R

0

=3Ω