Question

Resistance of a wire at \(0^\circ C\), \(100^\circ C\) and \(t^\circ C\) is found to be \(10 \, \Omega\), \(10.2 \, \Omega\) and \(10.95 \, \Omega\) respectively. The temperature \(t\) in Kelvin scale is ______.

Answer 1

Correct Answer: 748

The temperature dependence of resistance is given by:
\[R = R_0 (1 + \alpha \Delta T).\]
From $0^\circ \text{C}$ to $100^\circ \text{C}$:
\[\frac{\Delta R}{R_0} = \alpha \Delta T \implies \alpha = \frac{10.2 - 10}{10 \cdot 100} = 0.002.\]
From $0^\circ \text{C}$ to $t^\circ \text{C}$:
\[\frac{\Delta R}{R_0} = \alpha \Delta T \implies \Delta T = \frac{10.95 - 10}{10 \cdot 0.002}.\]
\[\Delta T = 475^\circ \text{C}.\]
Convert to Kelvin:
T = 475 + 273 = 748 K
Final Answer: $748 \, \text{K}$.