A copper wire has a resistance of 1.02 Ω at 20.0°C. What is its resistance at 60°C? The temperature coefficient of resistivity for copper is 0.0039 (C°)—1.
R = 1.02 + 0.0039*(60-20)= 1.176 Ohms.
Required urgent
To determine the resistance of a copper wire at a different temperature, we can use the temperature coefficient of resistivity for copper. This coefficient represents how much the resistivity of copper changes with temperature.
The formula to calculate the resistance change with temperature is:
ΔR = R₀ * α * ΔT
Where:
ΔR is the change in resistance
R₀ is the initial resistance at 20°C
α is the temperature coefficient of resistivity for copper (0.0039 C°⁻¹)
ΔT is the change in temperature (in this case, 60°C - 20°C = 40°C)
Let's calculate it step by step:
1. Calculate the change in resistance:
ΔR = R₀ * α * ΔT
= 1.02 Ω * 0.0039 (C°⁻¹) * 40°C
= 0.15912 Ω
2. Add the change in resistance to the initial resistance:
R60 = R₀ + ΔR
= 1.02 Ω + 0.15912 Ω
= 1.17912 Ω
Therefore, the resistance of the copper wire at 60°C is approximately 1.17912 Ω.
To find the resistance of the copper wire at 60°C, we can use the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R1 = Resistance at T1 (20.0°C)
α = Temperature coefficient of resistivity for copper (0.0039 (C°)—1)
T1 = Initial temperature (20.0°C)
T2 = Final temperature (60°C)
R2 = Resistance at T2 (unknown)
First, let's substitute the known values into the formula:
R2 = 1.02 Ω * (1 + 0.0039 (C°)—1 * (60°C - 20.0°C))
Now, let's calculate the temperature difference (T2 - T1):
T2 - T1 = 60°C - 20.0°C = 40°C
Substituting the temperature difference into the equation:
R2 = 1.02 Ω * (1 + 0.0039 (C°)—1 * 40°C)
Now, calculate the value inside the brackets:
1 + 0.0039 (C°)—1 * 40°C = 1 + 0.0039 (C°)—1 * 40 = 1 + 0.156 = 1.156
Substitute this value back into the equation:
R2 = 1.02 Ω * 1.156
Finally, calculate the resistance at 60°C:
R2 = 1.17712 Ω
Therefore, the resistance of the copper wire at 60°C is approximately 1.17712 Ω.