Answer :
To determine the appropriate size of electrical metallic tubing (EMT) to accommodate twenty 18 AWG XFF and eighteen 16 AWG XFF conductors, we need to refer to the National Electrical Code (NEC) tables that provide the maximum number of conductors allowed in various EMT sizes. This ensures compliance with safety and regulatory guidelines.
### Step-by-Step Solution
1. Find the Cross-Sectional Area of Each Conductor:
Conductors are measured in American Wire Gauge (AWG), and the cross-sectional area (CSA) for each type of conductor can be found in NEC Table 5 (for individual wire dimensions). Here are the CSAs for the given conductors:
- 18 AWG (XFF): The cross-sectional area is approximately 0.0131 square inches per conductor.
- 16 AWG (XFF): The cross-sectional area is approximately 0.0165 square inches per conductor.
2. Calculate the Total CSA Required:
- For twenty 18 AWG XFF conductors:
[tex]\[ \text{Total CSA for 18 AWG} = 20 \times 0.0131 = 0.262 \text{ square inches} \][/tex]
- For eighteen 16 AWG XFF conductors:
[tex]\[ \text{Total CSA for 16 AWG} = 18 \times 0.0165 = 0.297 \text{ square inches} \][/tex]
- Combine both:
[tex]\[ \text{Total CSA needed} = 0.262 + 0.297 = 0.559 \text{ square inches} \][/tex]
3. Choose the Appropriate EMT Size:
Next, we refer to NEC Chapter 9, Table 4, which gives us the allowable fill capacity for EMT. This table indicates the maximum cross-sectional area that can be occupied by conductors for different sizes of EMT. The table typically includes the following options (though actual tables should be consulted for precise values):
- 1/2 inch EMT: Approximately 0.122 square inches fill capacity
- 3/4 inch EMT: Approximately 0.213 square inches fill capacity
- 1 inch EMT: Approximately 0.346 square inches fill capacity
- 1 1/4 inch EMT: Approximately 0.598 square inches fill capacity
4. Determine the Smallest Suitable EMT Size:
We need the smallest EMT size that has a fill capacity equal to or greater than our calculated requirement of 0.559 square inches.
- 1/2 inch EMT: 0.122 square inches (insufficient)
- 3/4 inch EMT: 0.213 square inches (insufficient)
- 1 inch EMT: 0.346 square inches (insufficient)
- 1 1/4 inch EMT: 0.598 square inches (sufficient)
Therefore, the most appropriate EMT size for accommodating twenty 18 AWG and eighteen 16 AWG XFF conductors is 1 1/4 inch EMT.
This solution should ensure that the EMT has enough capacity to safely and effectively house the conductors according to NEC standards.
### Step-by-Step Solution
1. Find the Cross-Sectional Area of Each Conductor:
Conductors are measured in American Wire Gauge (AWG), and the cross-sectional area (CSA) for each type of conductor can be found in NEC Table 5 (for individual wire dimensions). Here are the CSAs for the given conductors:
- 18 AWG (XFF): The cross-sectional area is approximately 0.0131 square inches per conductor.
- 16 AWG (XFF): The cross-sectional area is approximately 0.0165 square inches per conductor.
2. Calculate the Total CSA Required:
- For twenty 18 AWG XFF conductors:
[tex]\[ \text{Total CSA for 18 AWG} = 20 \times 0.0131 = 0.262 \text{ square inches} \][/tex]
- For eighteen 16 AWG XFF conductors:
[tex]\[ \text{Total CSA for 16 AWG} = 18 \times 0.0165 = 0.297 \text{ square inches} \][/tex]
- Combine both:
[tex]\[ \text{Total CSA needed} = 0.262 + 0.297 = 0.559 \text{ square inches} \][/tex]
3. Choose the Appropriate EMT Size:
Next, we refer to NEC Chapter 9, Table 4, which gives us the allowable fill capacity for EMT. This table indicates the maximum cross-sectional area that can be occupied by conductors for different sizes of EMT. The table typically includes the following options (though actual tables should be consulted for precise values):
- 1/2 inch EMT: Approximately 0.122 square inches fill capacity
- 3/4 inch EMT: Approximately 0.213 square inches fill capacity
- 1 inch EMT: Approximately 0.346 square inches fill capacity
- 1 1/4 inch EMT: Approximately 0.598 square inches fill capacity
4. Determine the Smallest Suitable EMT Size:
We need the smallest EMT size that has a fill capacity equal to or greater than our calculated requirement of 0.559 square inches.
- 1/2 inch EMT: 0.122 square inches (insufficient)
- 3/4 inch EMT: 0.213 square inches (insufficient)
- 1 inch EMT: 0.346 square inches (insufficient)
- 1 1/4 inch EMT: 0.598 square inches (sufficient)
Therefore, the most appropriate EMT size for accommodating twenty 18 AWG and eighteen 16 AWG XFF conductors is 1 1/4 inch EMT.
This solution should ensure that the EMT has enough capacity to safely and effectively house the conductors according to NEC standards.
