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At what temperature will the resistance of a copper wire be three times its value at 0ºC? (Given Temperature coefficient of resistance for copper = 4x10⁻3ºC⁻1)
- 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 will the resistance of a copper wire be three time...
°C?
The resistance of a copper wire increases with temperature. The relationship between the resistance of a copper wire and its temperature is given by the following formula:
Rt = R0 (1 + αt)
where Rt is the resistance of the wire at temperature t, R0 is the resistance of the wire at 0°C, α is the temperature coefficient of resistance for copper (0.00428 per °C), and t is the temperature in °C.
To find the temperature at which the resistance of a copper wire is three times its value at 0°C, we can set Rt = 3R0 in the above formula and solve for t:
3R0 = R0 (1 + αt)
3 = 1 + αt
αt = 2
t = 2/α
Substituting the value of α = 0.00428 per °C, we get:
t = 2/0.00428 = 467.29°C
Therefore, the temperature at which the resistance of a copper wire is three times its value at 0°C is approximately 467.29°C.
The resistance of a copper wire increases with temperature. The relationship between the resistance of a copper wire and its temperature is given by the following formula:
Rt = R0 (1 + αt)
where Rt is the resistance of the wire at temperature t, R0 is the resistance of the wire at 0°C, α is the temperature coefficient of resistance for copper (0.00428 per °C), and t is the temperature in °C.
To find the temperature at which the resistance of a copper wire is three times its value at 0°C, we can set Rt = 3R0 in the above formula and solve for t:
3R0 = R0 (1 + αt)
3 = 1 + αt
αt = 2
t = 2/α
Substituting the value of α = 0.00428 per °C, we get:
t = 2/0.00428 = 467.29°C
Therefore, the temperature at which the resistance of a copper wire is three times its value at 0°C is approximately 467.29°C.
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Community Answer
At what temperature will the resistance of a copper wire be three time...
For temp. coeff (a)=4×10^-3,
3R=R(1+(a)t)
2/4×10^-3=t
t=500
3R=R(1+(a)t)
2/4×10^-3=t
t=500
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At what temperature will the resistance of a copper wire be three times its value at 0ºC? (Given Temperature coefficient of resistance for copper = 4x10⁻3ºC⁻1)a)400ºCb)450ºCc)500ºCd)550ºCCorrect answer is option 'C'. Can you explain this answer?
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