at 20 c a length of copper wire has a resistance of 5.0 . What is the resistance at 80c. Let .004=a for 20c.
R = 5 + 0.004(80-20) =
To find the resistance of the copper wire at 80°C, we can use the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R1 = Resistance at T1
R2 = Resistance at T2
α = Temperature coefficient of resistance
T1 = Initial temperature in °C
T2 = Final temperature in °C
Given:
R1 = 5.0 Ω
T1 = 20°C
T2 = 80°C
α = 0.004 (as given in the question)
Substituting the given values into the formula, we can calculate the resistance at 80°C:
R2 = 5.0 Ω * (1 + 0.004 * (80 - 20))
Simplifying the equation:
R2 = 5.0 Ω * (1 + 0.004 * 60)
R2 = 5.0 Ω * (1 + 0.24)
R2 = 5.0 Ω * 1.24
R2 = 6.2 Ω
Therefore, the resistance of the copper wire at 80°C is 6.2 Ω.
To determine the resistance of a copper wire at 80°C, you will need to use the temperature coefficient of copper, which is denoted by the symbol "α." In this case, you've given that α = 0.004 per degree Celsius (°C).
To begin, let's calculate the resistance at 20°C using the given value of a = 0.004 per °C.
Resistance at 20°C (R1) = 5.0 Ω
Now, we can use the formula for temperature-dependent resistance:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 is the resistance at the desired temperature (80°C),
R1 is the resistance at the initial temperature (20°C),
α is the temperature coefficient of copper, and
T2 and T1 are the desired and initial temperatures, respectively.
Plugging in the values:
R2 = 5.0 Ω * (1 + 0.004 * (80 - 20))
Calculating the expression inside the parentheses first:
R2 = 5.0 Ω * (1 + 0.004 * 60)
R2 = 5.0 Ω * (1 + 0.24)
R2 = 5.0 Ω * 1.24
R2 = 6.2 Ω
Therefore, the resistance of the copper wire at 80°C would be approximately 6.2 Ω.