Question:
At what temperature will the resistance of a copper wire become three times its value at 0°C? (Temperature coefficient of resistance for copper \( \alpha = 4 \times 10^{-3} /°C \))
At what temperature will the resistance of a copper wire become three times its value at 0°C? (Temperature coefficient of resistance for copper \( \alpha = 4 \times 10^{-3} /°C \))
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The resistance of a conductor increases linearly with temperature when the temperature coefficient of resistance is constant.
Updated On: Apr 22, 2026
- 400°C
- 450°C
- 500°C
- 550°C
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the formula for resistance change with temperature.
The resistance of a material changes with temperature according to the formula: \[ R_T = R_0 (1 + \alpha T) \] where: - \( R_T \) is the resistance at temperature \( T \), - \( R_0 \) is the resistance at 0°C, - \( \alpha \) is the temperature coefficient of resistance, and - \( T \) is the temperature in °C.
Step 2: Set up the equation.
We are asked to find the temperature at which the resistance is three times its value at 0°C. Hence, we set: \[ R_T = 3 R_0 \] Substitute this into the formula for \( R_T \): \[ 3 R_0 = R_0 (1 + \alpha T) \] Simplifying: \[ 3 = 1 + \alpha T \] \[ 3 - 1 = \alpha T \] \[ 2 = \alpha T \]
Step 3: Solve for temperature.
Now, substitute the given value for \( \alpha = 4 \times 10^{-3} /°C \): \[ T = \frac{2}{4 \times 10^{-3}} = 500°C \]
Step 4: Conclusion.
The temperature at which the resistance becomes three times its value at 0°C is \( 500°C \), which is option (3).
The resistance of a material changes with temperature according to the formula: \[ R_T = R_0 (1 + \alpha T) \] where: - \( R_T \) is the resistance at temperature \( T \), - \( R_0 \) is the resistance at 0°C, - \( \alpha \) is the temperature coefficient of resistance, and - \( T \) is the temperature in °C.
Step 2: Set up the equation.
We are asked to find the temperature at which the resistance is three times its value at 0°C. Hence, we set: \[ R_T = 3 R_0 \] Substitute this into the formula for \( R_T \): \[ 3 R_0 = R_0 (1 + \alpha T) \] Simplifying: \[ 3 = 1 + \alpha T \] \[ 3 - 1 = \alpha T \] \[ 2 = \alpha T \]
Step 3: Solve for temperature.
Now, substitute the given value for \( \alpha = 4 \times 10^{-3} /°C \): \[ T = \frac{2}{4 \times 10^{-3}} = 500°C \]
Step 4: Conclusion.
The temperature at which the resistance becomes three times its value at 0°C is \( 500°C \), which is option (3).
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