First slide

Temperature dependence

Question

The temperature coefficient of resistance of a wire is .00125°C^-1. At 300 K its resistance is one ohm. The asistance of the wire will be 2 ohm at

Moderate

A

1154 K
B

1100K
C

1400 K
D

1.1.27 K

Solution

$\begin{array}{l} R_{300} = R_{0} (1 + α \times 27) = 1 \\ R_{t} = R_{0} (1 + α \times t) = 2 \\ ∴ \frac{1 + 27 α}{1 + αt} = \frac{1}{2} or 2 + 54 α = 1 + αt \\ 2 + 54 (0 \cdot 00125) = 1 + (0 \cdot 00125) t \\ t = 854^{\circ} C = 1127 K \end{array}$

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