Answer :
- Convert Fahrenheit to Celsius: $158^{\circ} F = 70^{\circ} C$.
- Determine the base ampacity of No. 10 THW copper wire in free air: approximately 40 A.
- Apply a temperature correction factor of 0.82 for $70^{\circ} C$.
- Calculate the adjusted ampacity: $40 A \times 0.82 = 32.8 A$. The closest answer is $\boxed{31.9 A}$.
### Explanation
1. Problem Analysis
We are given a No. 10 copper wire with THW insulation in free air at an ambient temperature of $158^{\circ} F$. We need to find its approximate ampacity.
2. Temperature Conversion
First, we need to convert the ambient temperature from Fahrenheit to Celsius. Using the formula $C = (F - 32) \times \frac{5}{9}$, we have $C = (158 - 32) \times \frac{5}{9} = 126 \times \frac{5}{9} = 70^{\circ} C$.
3. Base Ampacity
Next, we need to find the base ampacity of a No. 10 THW copper wire in free air. According to the National Electrical Code (NEC), a typical value for this is approximately 40 A.
4. Temperature Correction
Now, we need to apply a temperature correction factor for the ambient temperature of $70^{\circ} C$. The correction factor depends on the specific insulation type and temperature rating. For THW insulation, a reasonable estimate for the correction factor at $70^{\circ} C$ is 0.82.
5. Adjusted Ampacity Calculation
To find the adjusted ampacity, we multiply the base ampacity by the temperature correction factor: $40 A \times 0.82 = 32.8 A$.
6. Final Answer
Comparing the adjusted ampacity to the given options, the closest value is 31.9 A.
### Examples
Understanding wire ampacity and temperature correction is crucial in electrical engineering for designing safe and efficient electrical systems. For example, when wiring a house, electricians must select the appropriate wire gauge based on the expected current draw of the appliances and lighting fixtures. They also need to consider the ambient temperature in the walls and ceilings to ensure that the wires do not overheat, which could lead to a fire. By correctly applying ampacity derating factors, they can ensure the electrical system operates safely under various conditions.
- Determine the base ampacity of No. 10 THW copper wire in free air: approximately 40 A.
- Apply a temperature correction factor of 0.82 for $70^{\circ} C$.
- Calculate the adjusted ampacity: $40 A \times 0.82 = 32.8 A$. The closest answer is $\boxed{31.9 A}$.
### Explanation
1. Problem Analysis
We are given a No. 10 copper wire with THW insulation in free air at an ambient temperature of $158^{\circ} F$. We need to find its approximate ampacity.
2. Temperature Conversion
First, we need to convert the ambient temperature from Fahrenheit to Celsius. Using the formula $C = (F - 32) \times \frac{5}{9}$, we have $C = (158 - 32) \times \frac{5}{9} = 126 \times \frac{5}{9} = 70^{\circ} C$.
3. Base Ampacity
Next, we need to find the base ampacity of a No. 10 THW copper wire in free air. According to the National Electrical Code (NEC), a typical value for this is approximately 40 A.
4. Temperature Correction
Now, we need to apply a temperature correction factor for the ambient temperature of $70^{\circ} C$. The correction factor depends on the specific insulation type and temperature rating. For THW insulation, a reasonable estimate for the correction factor at $70^{\circ} C$ is 0.82.
5. Adjusted Ampacity Calculation
To find the adjusted ampacity, we multiply the base ampacity by the temperature correction factor: $40 A \times 0.82 = 32.8 A$.
6. Final Answer
Comparing the adjusted ampacity to the given options, the closest value is 31.9 A.
### Examples
Understanding wire ampacity and temperature correction is crucial in electrical engineering for designing safe and efficient electrical systems. For example, when wiring a house, electricians must select the appropriate wire gauge based on the expected current draw of the appliances and lighting fixtures. They also need to consider the ambient temperature in the walls and ceilings to ensure that the wires do not overheat, which could lead to a fire. By correctly applying ampacity derating factors, they can ensure the electrical system operates safely under various conditions.