Question

a niklil coil has a resistance of 13ohm at 50°c .if the temperature cofficient of resistance at 0°c is 0.006/°c ,the resistance at 0°c is
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Answer 1

Explanation:

Concept:

Effect of Temperature on Resistance:

For pure metals, resistance increased with an increase in temperature, this is called the positive temperature coefficient of resistance.

For semiconductors and insulators, resistance increased with decreases in temperature and vice-versa, this is called the negative temperature coefficient of resistance.

Temperature Coefficient of Resistance:

Let a metallic conductor having resistance R0 at 0°C be heated at t°C and resistance become Rt.

Increased in temperature = ΔR = Rt – R0

An increase in Resistance (ΔR) depends on:

Directly proportional its initial resistance.

Directly proportional to the rise in temperature.

On the nature of the material.

∴ (Rt – R0) α (R × t)

or, (Rt – R0) = α R0 t ---(1)

Where α is constant and known as the temperature coefficient of resistance.

From equation (1)

∴ Rt = R0 (1 + α t)

Calculation:

Given that, R = 13 Ω, α = 0.006/°C

Tref = 0°C, T = 50°C

∴ t = T - Tref = 50 - 0 = 50°C

From above concept,

Rt = R0 (1 + α t)

13 = R0 (1 + 0.006 × 50)

13 = 1.3 × R0

Hence, the resistance at 0°C is will be 10 Ω

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