Question

The temperature coefficient of resistance of a wire is \( 0.00125 \, \text{K}^{-1} \). At 300K its resistance is 1 ohm. The resistance of the wire will be 2 ohms at

• A. 1154K
• B. 1100K
• C. 1400K
• D. 1127K

Hint:

Resistance increases with temperature based on the temperature coefficient. Use the linear relationship for calculations.

Answer 1

The Correct Option is B

Step 1: Temperature dependence of resistance.
The resistance of the wire at temperature \( T \) is given by: \[ R_T = R_0 [1 + \alpha (T - T_0)] \] where \( R_0 \) is the resistance at \( T_0 \), and \( \alpha \) is the temperature coefficient.

Step 2: Apply the formula.
Substituting the given values, we find the temperature \( T \) where the resistance is 2 ohms. Thus, the correct answer is option (B).

Final Answer: \[ \boxed{1100 \, \text{K}} \]