Let's break down the problem step-by-step: ### **Given:** - **Transformer size:** 45 kVA, 3-phase - **Primary voltage:** 480V - **Secondary voltage:** 208/120V (we'll use 208V, the line-to-line voltage) - **Secondary conductor length:** 10 feet - **Termination:** Panelboard with **one 3-pole breaker, 150A** - **Conductor type:** THHN copper - **Termination temperature rating:** 75°C --- ## **Step 1: Calculate the Full Load Current on the Secondary Side** The formula for 3-phase current is: \[ I = \frac{\text{Transformer kVA} \times 1000}{\sqrt{3} \times \text{Voltage}} \] Plug in the values: \[ I = \frac{45,000}{\sqrt{3} \times 208} \] \[ I = \frac{45,000}{360.8} \] \[ I ≈ 124.7 \text{ A} \] --- ## **Step 2: Determine the Minimum Conductor Ampacity Required** ### **NEC 240.21(C) – Protection of Transformer Secondary Conductors** For secondary conductors **not over 10 feet long**, you can use the "10-foot tap rule." The requirements for this rule include: - The ampacity of the secondary conductor is **not less than the combined calculated loads on the circuits supplied by the tap conductors**. - The tap conductors **terminate in a single circuit breaker** (which they do: a 150A breaker). - The ampacity of the secondary conductor **is not less than 1/10th of the rating of the overcurrent device**, but this is a minimum. **But** the conductors must always be sized for at least the load they serve. ### **What ampacity do we need?** - **Load on the transformer:** 124.7A (from Step 1) - **Breaker size:** 150A **Per the 10-foot tap rule** (NEC 240.21(C)(2)), the conductors must have an ampacity **not less than the load** (124.7A), and **not less than the rating of the breaker** if the tap conductors terminate in a single breaker (as here). **So, the conductors must be rated for at least 124.7A.** --- ## **Step 3: Select the Conductor Size Using NEC Table 310.16 (2023) [or 310.15(B)(16) in previous NECs]** **THHN copper at 75°C:** - **1 AWG:** 130A - **2 AWG:** 115A - **1/0 AWG:** 150A - **Our load:** 124.7A So, **2 AWG** is only good for 115A (not enough). **1 AWG** is good for 130A (meets the requirement). **1/0 AWG** is good for 150A (more than needed). --- ## **Step 4: Final Check – Does 1 AWG Meet All Rules?** - **Ampacity:** 130A (1 AWG), which is **greater than 124.7A**. - **Breaker:** 150A – per 240.21(C)(2), the tap can terminate in a single breaker rated no more than the ampacity of the conductors, which in this case is **not more than 10x the ampacity of the conductors**. 150A/130A = 1.15 (so it's less than 10x). - **Length:** 10 feet or less. - **Termination:** Single breaker. **All requirements satisfied.** --- ## **Step 5: Final Answer** ### **The minimum size THHN copper secondary conductors permitted for this transformer installation is:** \[ \boxed{1 \text{ AWG} \ \text{THHN copper}} \] at 75°C ampacity (130A). --- ### **Summary Table** | Conductor Size | 75°C Ampacity (THHN Cu) | Sufficient? | |----------------|------------------------|-------------| | 2 AWG | 115A | **No** | | 1 AWG | 130A | **Yes** | | 1/0 AWG | 150A | Yes | --- ### **References:** - NEC Table 310.16 (2023) / 310.15(B)(16) (older editions) - NEC 240.21(C)(2) – 10-foot tap rule --- **Final Answer:** \[ \boxed{\text{1 AWG THHN copper}} \] is the minimum size permitted for the secondary conductors in this scenario.

# Minimum Size THHN Copper Secondary Conductors Calculation ## **Given:** - **Transformer Size:** 45 kVA, 3-phase - **Primary Voltage:** 480V - **Secondary Voltage:** 208/120V (using 208V) - **Length of Secondary Conductors:** 10 feet - **Termination:** Panelboard with a 3-pole breaker rated at 150A - **Conductor Type:** THHN copper - **Temperature Rating:** 75°C --- ## **Step 1: Calculate Full Load Current on Secondary Side** Use the formula for 3-phase current: \[ I = \frac{\text{Transformer kVA} \times 1000}{\sqrt{3} \times \text{Voltage}} \] Calculating: \[ I = \frac{45,000}{\sqrt{3} \times 208} \approx \frac{45,000}{360.8} \approx 124.7 \text{ A} \] --- ## **Step 2: Determine Minimum Conductor Ampacity Required** ### **NEC 240.21(C) – Protection of Transformer Secondary Conductors** - For conductors **not over 10 feet long**, apply the "10-foot tap rule." - Ampacity of the secondary conductor must not be less than the calculated load (124.7A) or the rating of the breaker (150A). ### **Load vs. Breaker:** - **Calculated Load:** 124.7A - **Breaker Size:** 150A The conductors must meet the higher of these two values. --- ## **Step 3: Select Conductor Size from NEC Table 310.16** ### **THHN Copper at 75°C:** | Conductor Size | 75°C Ampacity | |----------------|----------------| | 2 AWG | 115A | | 1 AWG | 130A | | 1/0 AWG | 150A | - **2 AWG:** 115A (not sufficient) - **1 AWG:** 130A (sufficient) - **1/0 AWG:** 150A (exceeds requirement) --- ## **Step 4: Final Check for 1 AWG** - **Ampacity of 1 AWG:** 130A (greater than 124.7A) - **Breaker Rating:** 150A – meets the requirement of terminating at a single breaker. - **Length:** 10 feet or less. - **Termination:** Single breaker. All requirements are satisfied. --- ## **Final Answer** ### **The minimum size THHN copper secondary conductors permitted for this transformer installation is:** \[ \boxed{1 \text{ AWG} \ \text{THHN copper}} \] --- ### **Summary Table** | Conductor Size | 75°C Ampacity (THHN Cu) | Sufficient? | |----------------|--------------------------|-------------| | 2 AWG | 115A | No | | 1 AWG | 130A | Yes | | 1/0 AWG | 150A | Yes | --- ### **References:** - NEC Table 310.16 (2023) / 310.15(B)(16) (older editions) - NEC 240.21(C)(2) – 10-foot tap rule --- **Final Answer:** \[ \boxed{\text{1 AWG THHN copper}} \] is the minimum size permitted for the secondary conductors in this scenario.