Question

A silver wire has a resistance of 215 \(\Omega\) at 27.5°C and a resistance of 270 \(\Omega\) at 100°C. Then the temperature coefficient of the resistivity of silver will be ……

Hint:

The {temperature coefficient of resistivity} (\(\alpha\)) determines how much the resistance of a material changes with temperature. It is calculated using \( \alpha = \frac{R_2 - R_1}{R_1 (T_2 - T_1)} \).

Answer 1

Step 1: Understanding the Temperature Coefficient of Resistivity
The temperature coefficient of resistivity (\(\alpha\)) is given by: \[ \alpha = \frac{R_2 - R_1}{R_1 (T_2 - T_1)} \] where:
- \( R_1 \) = Initial resistance at \( T_1 \),
- \( R_2 \) = Final resistance at \( T_2 \),
- \( \alpha \) = Temperature coefficient of resistivity.
Step 2: Given Values
- \( R_1 = 215 \, \Omega \),
- \( R_2 = 270 \, \Omega \),
- \( T_1 = 27.5^\circ C \),
- \( T_2 = 100^\circ C \).
Step 3: Calculating \(\alpha\)
\[ \alpha = \frac{270 - 215}{215 \times (100 - 27.5)} \] \[ \alpha = \frac{55}{215 \times 72.5} \] \[ \alpha = \frac{55}{15587.5} \]