Question

An aluminium resistor has a resistance of 43.6 ohm at 20 0C and 50.8 ohm at 60 0C. Determine the temperature coefficient of resistance of aluminium at 0 0C, its resistance at 0 0C and at 40 0C.​

Answer 1

Explanation:

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

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