VIPSolutionsGive step-by-step solution with explanation and final answer: A 50-hp AC motor is connected to 230 volts. The motor does not contain a NEMAcode. The motor is expected to operate for more than three hours at a time. Theconductors are to be copper with type RHW-2 insulation. The motor is locatedin an area with an ambient temperature of 100 deg F. The two conductors are to berun in conduit. What size conductors should be used to connect this motor? (Note: 1 hp5 746 watts
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Give step-by-step solution with explanation and final answer: A 50-hp AC motor is connected to 230 volts. The motor does not contain a NEMAcode. The motor is expected to operate for more than three hours at a time. Theconductors are to be copper with type RHW-2 insulation. The motor is locatedin an area with an ambient temperature of 100 deg F. The two conductors are to berun in conduit. What size conductors should be used to connect this motor? (Note: 1 hp5 746 watts
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Asked by: ravi
Created at: 2025-08-13 20:46:44
Asked by: ravi
Created at: 2025-08-13 20:46:44
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Let's solve the problem step by step:
---
### **Step 1: Calculate the Full-Load Amperes (FLA) of the Motor**
Given:
- Motor Power = 50 hp
- 1 hp = 746 W
- Voltage = 230 V
- Assume 3-phase (since most motors of this size are 3-phase, but if it's single-phase, let me know—I'll solve for both!)
#### **A. Convert hp to Watts**
\[
50~\text{hp} \times 746~\frac{\text{W}}{\text{hp}} = 37,300~\text{W}
\]
#### **B. Calculate Full-Load Amps**
**For 3-phase:**
\[
I = \frac{P}{\sqrt{3} \times V \times \text{Efficiency} \times \text{Power Factor}}
\]
If efficiency and power factor are not given, use NEC Table 430.250 for motor FLA.
**NEC Table 430.250:**
- For 50 hp, 230 V, 3-phase, FLA = **130 A**
---
### **Step 2: Determine Conductor Ampacity Required**
#### **A. Per NEC 430.22**
- Conductors must be sized at **125% of the motor FLA**.
\[
\text{Minimum Conductor Ampacity} = 1.25 \times 130~\text{A} = 162.5~\text{A}
\]
---
### **Step 3: Apply Ambient Temperature Correction**
#### **A. Find Conductor Ampacity at 75°C (RHW-2 is 90°C rated, but terminals are often only rated 75°C)**
- **From NEC Table 310.16 (2023):**
- 1 AWG Cu: 110 A (75°C col)
- 2/0 AWG Cu: 175 A (75°C col)
- 3/0 AWG Cu: 200 A (75°C col)
We'll use 2/0 AWG as a candidate.
#### **B. Ambient Temperature Correction**
- **Ambient Temp:** 100°F = 38°C
- **From NEC Table 310.15(B)(1):**
- For 75°C conductors, 36–40°C: **0.91**
- Correction factor = 0.91
\[
\text{Corrected Ampacity} = 175~\text{A} \times 0.91 = 159.25~\text{A}
\]
This is **less than 162.5 A** required.
Try the next size up: **3/0 AWG (200 A at 75°C)**
\[
\text{Corrected Ampacity} = 200~\text{A} \times 0.91 = 182~\text{A}
\]
---
### **Step 4: Final Answer**
- **3/0 AWG Cu RHW-2** has a corrected ampacity of 182 A, which is greater than the required 162.5 A.
---
## **Final Answer**
### **You should use 3/0 AWG copper conductors with type RHW-2 insulation to connect this 50-hp, 230-volt motor, given the ambient temperature of 100°F.**
---
### **Summary of Steps:**
1. Found motor FLA from NEC Table 430.250 (130 A).
2. Multiplied by 125% per NEC 430.22 (162.5 A).
3. Checked ampacity for Type RHW-2 copper at 75°C, applied ambient (100°F) correction (factor 0.91).
4. 2/0 AWG was too small; 3/0 AWG is sufficient (corrected ampacity = 182 A).
**\(\boxed{3/0~\text{AWG}~\text{Cu, RHW-2}}\)**
is the correct minimum size for the conductors.
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