Question

Temperature coefficient of resistance is 0.00125 per°C. Given the resistance of wire at 300k is 1 ohm. What will be the temperature in K when resistance become 2 ohm.

Answer 1

Initial temperature = 300 K = 27°C

Resistance of wire is a linear function of temperature.
So,
α = ΔR / (RΔθ)
Δθ = ΔR / (Rα)
(T - 27) = (2 Ω - 1 Ω) / (1 Ω × 0.00125 /°C)
T - 27 °C = 800 °C
T = 27 °C + 800°C
T = 827 °C
T = (827 + 273) K
T = 1100 K

Temperature of wire will be 1100 K

Answer 2

27°C

Resistance of wire is a linear function of temperature.

So,

α = ΔR / (RΔθ)

Δθ = ΔR / (Rα)

(T - 27) = (2 Ω - 1 Ω) / (1 Ω × 0.00125 /°C)

T - 27 °C = 800 °C

T = 27 °C + 800°C

T = 827 °C

T = (827 + 273) K

T = 1100 K

Therefore the temperature of wire will be 1100 K.