Question

In an experiment to determine the temperature coefficient of resistance of a conductor, a coil of wire X is immersed in a liquid. It is heated by an external agent. A meter bridge set up is used to determine resistance of the coil X at different temperatures. The balancing points measured at temperatures \( t_1 = 0^\circ \text{C} \) and \( t_2 = 100^\circ \text{C} \) are 50 cm and 60 cm respectively. If the standard resistance taken out is \( S = 4 \, \Omega \) in both trials, the temperature coefficient of the coil is

• A. 0.05°C\(^{-1}\)
• B. 0.02°C\(^{-1}\)
• C. 0.005°C\(^{-1}\)
• D. 2.0°C\(^{-1}\)

Answer 1

The Correct Option is C

To determine the temperature coefficient of resistance, we use the formula:
\( \alpha = \frac{R_2 - R_1}{R_1 (T_2 - T_1)} \) where:
- \( R_1 = 4 \Omega \) is the resistance at \( t_1 = 0^\circ \text{C} \), 
- \( R_2 = 6 \Omega \) is the resistance at \( t_2 = 100^\circ \text{C} \), 
- \( T_1 = 0^\circ \text{C} \) and \( T_2 = 100^\circ \text{C} \). 
Now substitute the values into the formula:\( \alpha = \frac{6 - 4}{4 \times (100 - 0)} = \frac{2}{400} = 0.005°C^{-1} \)