A wire 3.00 m long and .450 mm2 in cross-sectional area has a resistance of 41.0Ω at 20 degrees C. If its resistance increases to 41.4Ω at 29.0 C, what is the temperature coefficient of resistivity?
R = Ro + aRo (T - To).
R = 41 + a41 (29 - 20) = 41.4 Ohms,
41 + 41a * 9 = 41.4,
41 + 369a = 41.4,
369a = 41.4 - 41 = 0.4,
a = 0.4 / 369 = 1.084*10^-3 = 0.001084 = Temperature coefficient of resistivity.
To find the temperature coefficient of resistivity (α), we can use the formula:
α = (R2 - R1) / (R1 * (T2 - T1))
Where:
R1 = resistance at temperature T1,
R2 = resistance at temperature T2,
T1 = initial temperature,
T2 = final temperature.
Given:
R1 = 41.0 Ω,
R2 = 41.4 Ω,
T1 = 20 °C,
T2 = 29 °C.
Let's substitute these values into the formula to calculate α:
α = (41.4 Ω - 41.0 Ω) / (41.0 Ω * (29 °C - 20 °C))
Simplifying,
α = 0.4 Ω / (41.0 Ω * 9 °C)
= 0.0049 Ω / °C
Therefore, the temperature coefficient of resistivity is 0.0049 Ω/°C.
To find the temperature coefficient of resistivity, we need to use the formula:
α = (ΔR / R₀) / (ΔT)
Where:
α is the temperature coefficient of resistivity (in °C⁻¹),
ΔR is the change in resistance (in Ω),
R₀ is the initial resistance (in Ω),
ΔT is the change in temperature (in °C).
Given:
Initial resistance, R₀ = 41.0 Ω
Change in resistance, ΔR = 41.4 Ω - 41.0 Ω = 0.4 Ω
Change in temperature, ΔT = 29.0 °C - 20.0 °C = 9.0 °C
Now, we can plug in these values into the formula:
α = (0.4 Ω / 41.0 Ω) / (9.0 °C) = 0.0098 °C⁻¹
Therefore, the temperature coefficient of resistivity is approximately 0.0098 °C⁻¹.