a metal wire has a resistance of 8 Ohms at a temperature of 20 degrees. if the same wire has a resistance of 8.40 Ohms at 70 degrees. What is the resistance of this wire in Ohms when its temperature is -10 degree celsius
To find the resistance of the wire at -10 degrees Celsius, we need to use the temperature coefficient of resistance for the wire material. The temperature coefficient of resistance (alpha) is a constant that represents the change in resistance per degree Celsius.
The formula to calculate the change in resistance due to temperature is:
ΔR = R * α * ΔT
Where:
ΔR is the change in resistance,
R is the initial resistance (at 20 degrees Celsius),
α is the temperature coefficient of resistance, and
ΔT is the change in temperature.
In this case, we know the initial resistance (8 Ohms) at 20 degrees Celsius, the final resistance (8.40 Ohms) at 70 degrees Celsius, and we want to find the resistance at -10 degrees Celsius.
First, let's calculate ΔR:
ΔR = 8.40 Ohms - 8 Ohms = 0.40 Ohms
Next, we need to calculate the change in temperature (ΔT) from 20 degrees Celsius to -10 degrees Celsius:
ΔT = -10 degrees Celsius - 20 degrees Celsius = -30 degrees Celsius
Now, we need to find the temperature coefficient of resistance (α) for the wire material. This value is usually provided or can be looked up in a reference table. Let's assume α = 0.00393 per degree Celsius for the wire material.
Using the formula, we can now find the resistance at -10 degrees Celsius:
ΔR = R * α * ΔT
0.40 Ohms = 8 Ohms * 0.00393 per degree Celsius * (-30 degrees Celsius)
Solving for R:
R = ΔR / (α * ΔT)
R = (0.40 Ohms) / (0.00393 per degree Celsius * -30 degrees Celsius)
R ≈ 3.22 Ohms
Therefore, the resistance of the wire at -10 degrees Celsius is approximately 3.22 Ohms.
To solve this problem, we can use the formula for temperature coefficient of resistance (α):
ΔR = R₀ * α * ΔT
Where:
ΔR is the change in resistance
R₀ is the initial resistance at temperature T₀
α is the temperature coefficient of resistance
ΔT is the change in temperature
First, let's find the change in resistance at a temperature increase from 20 degrees to 70 degrees:
ΔR = 8.40 Ohms - 8 Ohms
ΔR = 0.40 Ohms
Next, we'll need to find the temperature coefficient of resistance (α) for this wire. The temperature coefficient of resistance is a material-specific constant typically given in units of ohms per degree Celsius (Ω/°C). Unfortunately, you haven't provided the value of α for this wire. The value can vary depending on the type of metal used in the wire.
Once you have the value of α, you can use it to calculate the resistance change for a different temperature change. For example, to find the resistance at -10 degrees Celsius, you would substitute the values into the formula:
ΔR = R₀ * α * ΔT
Where:
ΔR is the change in resistance
R₀ is the initial resistance at temperature T₀ (in this case, 8.40 Ohms)
α is the temperature coefficient of resistance
ΔT is the change in temperature (from 70 degrees to -10 degrees)
If you provide the value of α for the wire, I can help you calculate the resistance at -10 degrees Celsius.
R₀=8 Ω, T₀=20℃,
R₁=8.4 Ω, T₁=70℃,
T₂ = - 10℃
R₂=?
R=R₀[1-αΔT]
R₁=R₀[1-αΔT₁]
8.4=8[1+(70-20)α]
α={8.4/8 – 1)/50 = 10⁻³ K⁻¹
R₂=R₀[1-αΔT₂] =
=8[1+ 10⁻³•(-10-20)] =7.76 Ω