Question

calculate the resistance of conductor at 100°C.if it's resistance is 5 omega at zero d egre celsius and temperature coefficient of resistance is 0.3*10^4​

Answer 1

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12th

Physics

Current Electricity

Temperature Dependence of Resistance

The resistance of a conduct...

PHYSICS

The resistance of a conductor at 20

o

C is 3.15 ohm and at 100

o

C is 3.75ohm. Determine the temperature co-efficient of resistance of the conductor. What will be the resistance of the conductor at 0

o

C?

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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

∘

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.

Answer 2

Given:

✭ Initial temperature (t₀) = 0° C

✭ Final temperature (t) = 100° C

✭ Initial resistance (R₀) = 5 Ω

✭ Coefficent of resistance (α) = 0.3 × 10⁻⁴

To Find:

◈ Final resistance (R)?

Solution:

We have to find the resistance of the conductor at 100°C

The final resistance is given by

R = R₀ × (1 + α (t - t₀))

Substitute the data,

➝ R = 5 × (1 + 0.3 × 10⁻⁴ (100 - 0))

➝ R = 5 × ( 1 + 0.3 × 10⁻⁴ × 10²)

➝ R = 5 × (1 + 0.3 × 10⁻²)

➝ R = 5 × (1.003)

➝ R = 5.015 Ω

Therefore the resistance of the conductor is 5.015

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☯ Know More

• The temperature coefficient of resistance(α) is defined as the increase in resistance per unit original distance per degree celsius or Kelvin rise of temperature.
• In case of metallic conductors, α is positive value, If temperature increases, resistance increases
• In case of semi conductors and insulators, α is negative value. If temperature increases, resistance decreases.
• In case of alloys like constantan and manganin, α is very small. If temperature increases, resistance does not change much

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