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At what temperature, the resistance of a copper wire will become three times its value at 0ºC ? (Temperature coefficient of resistance for copper = 4 x 10⁻3per ºC)
- a)400ºC
- b)450ºC
- c)500ºC
- d)550ºC
Correct answer is option 'C'. Can you explain this answer?
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At what temperature, the resistance of a copper wire will become three...
The resistance of a copper wire increases with temperature. The relationship between resistance and temperature can be approximated using the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 = new resistance
R1 = initial resistance (at 0°C)
α = temperature coefficient of resistance for copper (approximately 0.00393 per °C)
T2 = new temperature
T1 = initial temperature (0°C)
To find the temperature at which the resistance becomes three times its value at 0°C, we can set R2 = 3R1 in the formula:
3R1 = R1 * (1 + α * (T2 - 0))
Simplifying the equation:
3 = 1 + αT2
2 = αT2
T2 = 2 / α
Using the approximate value for α (0.00393 per °C), we can calculate T2:
T2 = 2 / 0.00393
T2 ≈ 508.9 °C
Therefore, the temperature at which the resistance of a copper wire will become three times its value at 0°C is approximately 508.9 °C.
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 = new resistance
R1 = initial resistance (at 0°C)
α = temperature coefficient of resistance for copper (approximately 0.00393 per °C)
T2 = new temperature
T1 = initial temperature (0°C)
To find the temperature at which the resistance becomes three times its value at 0°C, we can set R2 = 3R1 in the formula:
3R1 = R1 * (1 + α * (T2 - 0))
Simplifying the equation:
3 = 1 + αT2
2 = αT2
T2 = 2 / α
Using the approximate value for α (0.00393 per °C), we can calculate T2:
T2 = 2 / 0.00393
T2 ≈ 508.9 °C
Therefore, the temperature at which the resistance of a copper wire will become three times its value at 0°C is approximately 508.9 °C.
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At what temperature, the resistance of a copper wire will become three times its value at 0ºC ? (Temperature coefficient of resistance for copper = 4 x 103per ºC)a)400ºCb)450ºCc)500ºCd)550ºCCorrect answer is option 'C'. Can you explain this answer?
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