A length of copper telephone line has a resistance of 24Ω at 20 degree Celsius. What it its resistance on a hot summer day when its temperature rises to 36 degree Celsius.
To find the resistance of the copper telephone line at a temperature of 36 degrees Celsius, we can use the formula for temperature-dependent resistance:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 = Resistance at the second temperature (36 degrees Celsius)
R1 = Resistance at the first temperature (20 degrees Celsius)
α = Temperature coefficient of copper (which is 0.00393 per degree Celsius)
T2 = Second temperature (36 degrees Celsius)
T1 = First temperature (20 degrees Celsius)
Let's substitute the values into the formula:
R2 = 24Ω * (1 + 0.00393 * (36 - 20))
Now, let's calculate the result step-by-step:
1. Calculate the difference in temperature:
36 - 20 = 16 degrees Celsius
2. Multiply the temperature difference by the temperature coefficient:
16 * 0.00393 = 0.06288
3. Add 1 to the result:
0.06288 + 1 = 1.06288
4. Multiply the resistance at the first temperature (24Ω) by the result:
24 * 1.06288 ≈ 25.55Ω
Therefore, the resistance of the copper telephone line on a hot summer day when the temperature is 36 degrees Celsius is approximately 25.55Ω.
To determine the resistance of the copper telephone line at a higher temperature, we need to consider the temperature coefficient of resistance for copper. The temperature coefficient of resistance is given by the formula:
α = 0.00428 Ω/Ω/°C
Where α is the temperature coefficient of resistance for copper.
Next, we need to determine the change in temperature (ΔT) by subtracting the initial temperature (20°C) from the final temperature (36°C):
ΔT = Tfinal - Tinitial
ΔT = 36°C - 20°C
ΔT = 16°C
Now, we can calculate the change in resistance (ΔR) using the formula:
ΔR = α * Rinitial * ΔT
Where Rinitial is the initial resistance of the copper telephone line (24Ω).
Substituting the given values into the formula:
ΔR = 0.00428 Ω/Ω/°C * 24Ω * 16°C
ΔR ≈ 2.0656Ω
Finally, we can find the resistance on a hot summer day by adding the change in resistance (ΔR) to the initial resistance (Rinitial):
Rfinal = Rinitial + ΔR
Rfinal = 24Ω + 2.0656Ω
Rfinal ≈ 26.07Ω
Therefore, the resistance of the copper telephone line on a hot summer day when its temperature rises to 36°C is approximately 26.07Ω.