Question

The resistance of a conductor is 6 ohm at 50 degree Celsius and 7 ohm at hundred degree Celsius calculate coefficient of resistance and find the resistance of conductor at zero degree celsius

Answer 1

Answer:

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Answer 2

Concept:

• The relation between temperature and resistance of a material

Given:

• Resistance of conductor at T1 = 50°C R1 = 6 ohm
• Resistance of conductor at T2 = 100°C R2 = 7 ohm

Find:

• The coefficient of resistance
• The resistance of the conductor at 0°C

Solution:

Rt = R₀ (1+ αΔT)

Let R₀ be the resistance of the conductor at 0°C

R1 = R₀ (1+ 50α)

6 = R₀ (1+ 50α)

6/(1+ 50α) = R₀

R2 =  R₀ (1+ 100α)

7 =  R₀ (1+ 100α)

7/(1+ 100α) = R₀

6/(1+ 50α) = R₀ = 7/(1+ 100α)

6/(1+ 50α) = 7/(1+ 100α)

6 (1+ 100α) = 7 (1+ 50α)

6 + 600α = 7 + 350α

250 α = 1

α = 1/250

α = 0.004

6 = R₀ (1+ 50α)

6 = R₀ (1+ 50(0.004))

6 = 1.2R₀

R₀ = 6/1.2 = 5 ohm

The coefficient of resistance is 0.004/ °C  and the resistance of the conductor at 0°C is 5 ohm.

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