The resistance of a coil copper wire at 20 degree celsius is 2.21 ohms. After a current of 10 amperes has been flowing in wire for two hours, the resistance of the coil was found o be 2.59 ohms. What is the temperature rise?
To find the temperature rise, we can use the formula for resistance change due to temperature:
ΔR = αR₀ΔT
Where:
ΔR = Change in resistance
α = Temperature coefficient of resistance
R₀ = Initial resistance
ΔT = Change in temperature
First, let's calculate the change in resistance (ΔR):
ΔR = R - R₀
= 2.59 Ω - 2.21 Ω
= 0.38 Ω
Next, let's find the temperature coefficient of resistance (α) for copper. The temperature coefficient of resistance for copper is approximately 0.0039 per degree Celsius.
Now, substitute the values into the formula:
0.38 Ω = (0.0039/°C) × 2.21 Ω × ΔT
To find ΔT, divide both sides of the equation by (0.0039/°C) × 2.21 Ω:
ΔT = 0.38 Ω / ((0.0039/°C) × 2.21 Ω)
Now, calculate ΔT:
ΔT ≈ 97.64 °C.
Therefore, the temperature rise in the copper wire is approximately 97.64 degrees Celsius.
To find the temperature rise, we need to calculate the change in resistance and then use the temperature coefficient of resistance for copper wire to relate it to the temperature rise. The formula to calculate the temperature rise is:
Temperature Rise = (Change in Resistance / Initial Resistance) / Temperature Coefficient of Resistance
Step 1: Calculate the change in resistance.
Change in Resistance = Final Resistance - Initial Resistance = 2.59 ohms - 2.21 ohms = 0.38 ohms
Step 2: Calculate the temperature coefficient of resistance for copper wire.
The temperature coefficient of resistance for copper wire is typically around 0.00393 per degree Celsius.
Step 3: Calculate the temperature rise using the formula.
Temperature Rise = (0.38 ohms / 2.21 ohms) / 0.00393 per °C
Temperature Rise ≈ 0.172 / 0.00393 ≈ 43.72°C
Therefore, the temperature rise is approximately 43.72 degrees Celsius.
The Temperature Coefficient of Copper (near
room temperature) is +0.393 % per o
C. This
means if the temperature increases 1o
C the
resistance will increase 0.393%.
does that help?