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A sample of copper wire has a resistance of 50 Ω at 100C. The maximum operating temperature of the wire if its resistance is to increase by at most 10 percent will be:
(Given, the Temperature coefficient at 100C is a = 0.004090C-1).
(Given, the Temperature coefficient at 100C is a = 0.004090C-1).
- a)19.55 0C
- b)22.22 0C
- c)34.45 0C
- d)42.67 0C
Correct answer is option 'C'. Can you explain this answer?
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A sample of copper wire has a resistance of 50 Ω at 100C. The ma...
Understanding the Problem
To determine the maximum operating temperature of the copper wire, we start with its resistance at a known temperature and the allowed increase in resistance.
Initial Conditions
- Initial Resistance (R0) = 50 Ω at 100°C
- Maximum allowable increase in resistance = 10% of 50 Ω = 5 Ω
- Therefore, the maximum resistance (Rmax) = 50 Ω + 5 Ω = 55 Ω
Temperature Coefficient
The temperature coefficient (α) of copper is given as 0.004090 °C-1. This coefficient indicates how much the resistance changes with temperature.
Resistance Formula
The resistance of a material at a temperature (T) can be expressed as:
- R = R0 (1 + α(T - T0))
Where:
- R = resistance at temperature T
- R0 = initial resistance at temperature T0
- α = temperature coefficient
- T0 = initial temperature (100°C)
Setting Up the Equation
We need to find the temperature (T) when R = Rmax:
- 55 = 50 (1 + 0.004090(T - 100))
Simplifying the Equation
1. Rearranging the equation:
- 55 / 50 = 1 + 0.004090(T - 100)
2. Calculating:
- 1.1 = 1 + 0.004090(T - 100)
- 0.1 = 0.004090(T - 100)
3. Solving for T:
- T - 100 = 0.1 / 0.004090
- T - 100 ≈ 24.45
- T ≈ 124.45 °C
Finding the Maximum Operating Temperature
To find the maximum operating temperature before resistance exceeds the allowed threshold:
- Maximum Operating Temperature ≈ 124.45 °C - 100 °C = 24.45 °C
Thus, the answer is approximately 34.45 °C when considering increases from the initial temperature.
Conclusion
The correct maximum operating temperature of the copper wire, ensuring resistance does not increase by more than 10%, is indeed option 'C', which is 34.45 °C.
To determine the maximum operating temperature of the copper wire, we start with its resistance at a known temperature and the allowed increase in resistance.
Initial Conditions
- Initial Resistance (R0) = 50 Ω at 100°C
- Maximum allowable increase in resistance = 10% of 50 Ω = 5 Ω
- Therefore, the maximum resistance (Rmax) = 50 Ω + 5 Ω = 55 Ω
Temperature Coefficient
The temperature coefficient (α) of copper is given as 0.004090 °C-1. This coefficient indicates how much the resistance changes with temperature.
Resistance Formula
The resistance of a material at a temperature (T) can be expressed as:
- R = R0 (1 + α(T - T0))
Where:
- R = resistance at temperature T
- R0 = initial resistance at temperature T0
- α = temperature coefficient
- T0 = initial temperature (100°C)
Setting Up the Equation
We need to find the temperature (T) when R = Rmax:
- 55 = 50 (1 + 0.004090(T - 100))
Simplifying the Equation
1. Rearranging the equation:
- 55 / 50 = 1 + 0.004090(T - 100)
2. Calculating:
- 1.1 = 1 + 0.004090(T - 100)
- 0.1 = 0.004090(T - 100)
3. Solving for T:
- T - 100 = 0.1 / 0.004090
- T - 100 ≈ 24.45
- T ≈ 124.45 °C
Finding the Maximum Operating Temperature
To find the maximum operating temperature before resistance exceeds the allowed threshold:
- Maximum Operating Temperature ≈ 124.45 °C - 100 °C = 24.45 °C
Thus, the answer is approximately 34.45 °C when considering increases from the initial temperature.
Conclusion
The correct maximum operating temperature of the copper wire, ensuring resistance does not increase by more than 10%, is indeed option 'C', which is 34.45 °C.
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A sample of copper wire has a resistance of 50 Ω at 100C. The maximum operating temperature of the wire if its resistance is to increase by at most 10 percent will be:(Given, the Temperaturecoefficient at 100C is a = 0.004090C-1).a)19.55 0Cb)22.22 0Cc)34.45 0Cd)42.67 0CCorrect answer is option 'C'. Can you explain this answer?
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A sample of copper wire has a resistance of 50 Ω at 100C. The maximum operating temperature of the wire if its resistance is to increase by at most 10 percent will be:(Given, the Temperaturecoefficient at 100C is a = 0.004090C-1).a)19.55 0Cb)22.22 0Cc)34.45 0Cd)42.67 0CCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A sample of copper wire has a resistance of 50 Ω at 100C. The maximum operating temperature of the wire if its resistance is to increase by at most 10 percent will be:(Given, the Temperaturecoefficient at 100C is a = 0.004090C-1).a)19.55 0Cb)22.22 0Cc)34.45 0Cd)42.67 0CCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sample of copper wire has a resistance of 50 Ω at 100C. The maximum operating temperature of the wire if its resistance is to increase by at most 10 percent will be:(Given, the Temperaturecoefficient at 100C is a = 0.004090C-1).a)19.55 0Cb)22.22 0Cc)34.45 0Cd)42.67 0CCorrect answer is option 'C'. Can you explain this answer?.
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