Question

The resistance of a wire is \(2.5 \Omega\) at a temperature \(373 K\). If the temperature coefficient of resistance of the material of the wire is \(3.6 \times 10^{-3} K^{-1}\), its resistance at a temperature \(273 K\) is nearly: 

• A. \( 1.84 \Omega \)
• B. \( 2.46 \Omega \)
• C. \( 0.82 \Omega \)
• D. \( 4.58 \Omega \)

Hint:

The resistance of a conductor decreases with decreasing temperature. The temperature coefficient of resistance determines how much the resistance changes per unit temperature change.

Answer 1

The Correct Option is A

Step 1: Using the Temperature Dependence Formula 
The resistance of a wire at a given temperature is given by: \[ R_T = R_0 \left(1 + \alpha (T - T_0) \right) \] where: - \( R_T \) = Resistance at temperature \( T \), - \( R_0 = 2.5 \Omega \) (Resistance at reference temperature \( T_0 = 373K \)), - \( \alpha = 3.6 \times 10^{-3} K^{-1} \) (Temperature coefficient of resistance), - \( T = 273K \) (New temperature). 

Step 2: Substituting the Values 
\[ R_{273} = 2.5 \left( 1 + (3.6 \times 10^{-3} \times (273 - 373)) \right) \] \[ R_{273} = 2.5 \left( 1 + (3.6 \times 10^{-3} \times (-100)) \right) \] \[ R_{273} = 2.5 \left( 1 - 0.36 \right) \] \[ R_{273} = 2.5 \times 0.64 \] \[ R_{273} = 1.84 \Omega. \] 

Step 3: Conclusion 
Thus, the resistance of the wire at \( 273 K \) is: \[ \boxed{1.84 \Omega} \]