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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)400 oC
- b)450 oC
- c)500 oC
- d)550 oC
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...
Given, temperature coefficient of resistance for copper, α = 4 x 10^-3 per oC
Let R be the resistance of the copper wire at 0oC.
We need to find the temperature at which the resistance of the wire becomes three times its value at 0oC.
Let the temperature at which the resistance becomes three times be T.
We know that the resistance of a material changes with temperature, and this change can be given by the formula:
R = R0 (1 + αΔT)
where R0 is the resistance at temperature T0, α is the temperature coefficient of resistance, and ΔT is the change in temperature from T0.
Using this formula, we can write:
3R = R0 (1 + αΔT)
Dividing both sides by R0, we get:
3 = 1 + αΔT
αΔT = 2
ΔT = 2/α
Substituting the values of α and R0, we get:
ΔT = 2/(4 x 10^-3) = 500oC
Therefore, the temperature at which the resistance of the copper wire becomes three times its value at 0oC is 500oC, which is option (c).
Let R be the resistance of the copper wire at 0oC.
We need to find the temperature at which the resistance of the wire becomes three times its value at 0oC.
Let the temperature at which the resistance becomes three times be T.
We know that the resistance of a material changes with temperature, and this change can be given by the formula:
R = R0 (1 + αΔT)
where R0 is the resistance at temperature T0, α is the temperature coefficient of resistance, and ΔT is the change in temperature from T0.
Using this formula, we can write:
3R = R0 (1 + αΔT)
Dividing both sides by R0, we get:
3 = 1 + αΔT
αΔT = 2
ΔT = 2/α
Substituting the values of α and R0, we get:
ΔT = 2/(4 x 10^-3) = 500oC
Therefore, the temperature at which the resistance of the copper wire becomes three times its value at 0oC is 500oC, which is option (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 10-3per oC)a)400oCb)450oCc)500oCd)550oCCorrect answer is option 'C'. Can you explain this answer?
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