A commercial office building has a total calculated general lighting load of 30,000 VA and a total receptacle load of 15,000 VA. The building operates at 208Y/120V, three-phase. What is the total calculated current for the service feeder (in amperes)?

Correct answer: A. 144.2 A

First, sum the total VA load: 30,000 VA (lighting) + 15,000 VA (receptacles) = 45,000 VA. For a three-phase system, the current (I) is calculated using the formula I = VA / (V_line_to_line * √3). So, I = 45,000 VA / (208V * 1.732) = 45,000 VA / 360.256 V ≈ 124.91 A. However, the options are higher. Let's re-check the demand factors. For general lighting, there's a demand factor from table 220.42. For 30,000 VA, it's 100% of the first 3000 VA, then 35% of the next 117,000 VA. So, 3000 VA * 1.0 + (30,000 - 3000) * 0.35 = 3000 + 27000 * 0.35 = 3000 + 9450 = 12,450 VA for lighting. For receptacle load, NEC 220.44 states that for receptacle loads over 10 kVA, 10 kVA at 100% plus 50% of the excess over 10 kVA. So, 10,000 VA * 1.0 + (15,000 VA - 10,000 VA) * 0.50 = 10,000 VA + 5,000 VA * 0.50 = 10,000 VA + 2,500 VA = 12,500 VA for receptacles. Total demand VA = 12,450 VA (lighting) + 12,500 VA (receptacles) = 24,950 VA. Now, calculate current: I = 24,950 VA / (208V * √3) = 24,950 VA / 360.256 V ≈ 69.25 A. This is not matching any option. Let me re-read the question and assumed demand factors. The question states 'total calculated general lighting load' and 'total receptacle load', which often implies these are already demand-factored values unless otherwise specified. If these are already demand-factored or actual connected loads, then the initial calculation of 45,000 VA combined load is correct. I = 45,000 VA / (208V * √3) = 45,000 VA / (208V * 1.732) = 45,000 VA / 360.256 V = 124.91 A. This is very close to 125.0 A (Option B). Let's recheck the options and question. If the question implies the loads are the *total connected* loads, and demand factors need to be applied, then the calculation becomes more complex. However, if 'total calculated' means the final VA load *after* demand factors (where applicable), then the direct sum is used. In typical exam questions, 'total calculated load' refers to the demand load. Let's assume the question means total connected load and apply demand factors. Let's re-evaluate the assumption that 'total calculated' implies already demand-factored. Usually, 'total calculated load' means the final demand load after all factors. If it means 'total connected load before demand factors', then the prior calculation of 69.25A is correct. However, 125A is a common answer for such questions where the sum is directly used. Let's assume the question implicitly refers to the *connected* load and requires demand factors to be applied per NEC 220.42 and 220.44. Lighting: 30,000 VA First 3,000 VA @ 100% = 3,000 VA Remaining (30,000 - 3,000) = 27,000 VA @ 35% = 9,450 VA Total Lighting Demand = 3,000 + 9,450 = 12,450 VA Receptacles: 15,000 VA First 10,000 VA @ 100% = 10,000 VA Remaining (15,000 - 10,000) = 5,000 VA @ 50% = 2,500 VA Total Receptacle Demand = 10,000 + 2,500 = 12,500 VA Total Demand VA = 12,450 VA + 12,500 VA = 24,950 VA Current (I) = VA / (V_line_to_line * √3) I = 24,950 VA / (208V * 1.732) I = 24,950 VA / 360.256 I ≈ 69.25 A None of the options match this calculation. This indicates that the initial interpretation of 'total calculated general lighting load' and 'total receptacle load' means the *final demand loads* after any applicable demand factors have already been applied, or that the question is simpler and just asks for the current based on the given VA values as if they are already the demand values. Let's assume the simplest interpretation: the given VA values are the demand values to be used for the current calculation. Total VA = 30,000 VA (lighting) + 15,000 VA (receptacles) = 45,000 VA. For a three-phase system, current (I) = VA / (V_line_to_line * √3). I = 45,000 VA / (208V * 1.732) I = 45,000 VA / 360.256 I ≈ 124.91 A This is very close to Option B: 125.0 A. This suggests that the question implies the given loads are already demand-factored or are to be treated as such for the calculation. However, let's consider another common scenario in commercial buildings where general lighting is considered continuous (125% factor) and receptacles might have a demand factor. But the question asks for 'total calculated current', implying a direct calculation from the given VA. Let's revisit the options and the problem statement. If the answer is A, 144.2 A, how can we get that? 144.2 A * 208V * 1.732 = 51,999 VA. So, the total VA would be 52,000 VA. How to get 52,000 VA from 30,000 VA and 15,000 VA? If the 30,000 VA lighting load is continuous, it would be 30,000 VA * 1.25 = 37,500 VA. If the 15,000 VA receptacle load is treated at 100% (as it's often a 'calculated' load), then 37,500 VA + 15,000 VA = 52,500 VA. Current = 52,500 VA / (208V * 1.732) = 52,500 VA / 360.256 = 145.73 A. This is close to 144.2 A. This implies the lighting load is continuous and the receptacle load is taken at face value as a 'calculated' demand. Let's verify this interpretation. NEC 215.2(A)(1) states that feeders shall have an ampacity not less than required to supply the loads. For continuous loads, the minimum feeder ampacity shall be 125% of the continuous load. General lighting in commercial buildings is typically considered continuous. So, Lighting Demand = 30,000 VA * 1.25 = 37,500 VA. Receptacle Demand = 15,000 VA (assuming this is already a demand-factored value or a non-continuous load to be taken at face value for feeder calculation, as it's stated 'total receptacle load'). Total VA = 37,500 VA + 15,000 VA = 52,500 VA. Current (I) = Total VA / (Line-to-Line V * √3) I = 52,500 VA / (208V * 1.732) I = 52,500 VA / 360.256 I ≈ 145.73 A. This value is closest to 144.2 A (Option A). The discrepancy might be due to rounding of √3 or the options themselves are rounded. Let's assume 144.2 A is the intended answer based on 125% for lighting and 100% for receptacles. Final Calculation: 1. Lighting load (continuous): 30,000 VA * 1.25 = 37,500 VA 2. Receptacle load: 15,000 VA (taken as given demand) 3. Total VA demand = 37,500 VA + 15,000 VA = 52,500 VA 4. Three-phase current (I) = VA / (V_LL * √3) = 52,500 VA / (208V * 1.732) = 52,500 VA / 360.256 ≈ 145.73 A. Given the options, 144.2 A is the closest, implying some rounding in the problem's expected answer or a slightly different interpretation of √3. Let's re-calculate with 144.2 A * 208 * 1.732 = 51999 VA. So 52,000 VA is the target. If 30,000 VA * 1.25 = 37,500 VA. Remaining VA needed = 52,000 - 37,500 = 14,500 VA. This means the receptacle load would be 14,500 VA, not 15,000 VA. However, if we use the exact value 52,500 VA and the options, 144.2 A is the closest. Let's re-evaluate the initial assumption that 'total calculated general lighting load' and 'total receptacle load' are already demand-factored. If so, then 45,000 VA / (208 * √3) = 124.91 A. This is very close to 125.0 A. The phrasing 'total calculated general lighting load' and 'total receptacle load' is ambiguous. If it means 'total connected load before demand factors', then: Lighting: 3000 VA + (27000 * 0.35) = 12,450 VA Receptacles: 10000 VA + (5000 * 0.5) = 12,500 VA Total VA = 24,950 VA. Current = 24,950 / (208*1.732) = 69.25A. Not an option. If it means 'total connected continuous load' for lighting and 'total connected non-continuous load' for receptacles: Lighting: 30,000 VA * 1.25 = 37,500 VA (due to continuous nature, NEC 215.2(A)(1)) Receptacles: 15,000 VA (not continuous, or already demand factored to this value) Total VA = 37,500 + 15,000 = 52,500 VA Current = 52,500 / (208 * 1.732) = 145.73 A. Closest to 144.2 A. This interpretation (continuous lighting, non-continuous receptacles) is the most common for commercial buildings. So, the correct answer should be A, 144.2 A. The exact calculation is 52,500 VA / (208 * √3) = 145.73 A. The option 144.2 A is approximately 52000 VA. This could be due to rounding in the question or options. Assuming 144.2 A is the intended answer for a 52,000 VA total load. Let's re-confirm that 144.2 A * 208V * 1.732 = 52000 VA (approx). So, 52000 VA is the target. If lighting is 30,000 VA * 1.25 = 37,500 VA. Then receptacle must be 52,000 - 37,500 = 14,500 VA. The question states 15,000 VA. This small discrepancy suggests rounding or a slightly different interpretation. However, 145.73 A is definitively the result of 30k*1.25 + 15k. So, 144.2 A is the closest option. Let's go with the interpretation that general lighting is continuous (125% factor) and the receptacle load is given as its demand value. Lighting demand = 30,000 VA * 1.25 = 37,500 VA. Receptacle demand = 15,000 VA. Total demand = 37,500 VA + 15,000 VA = 52,500 VA. Current = 52,500 VA / (208V * √3) = 52,500 VA / (208V * 1.732) = 52,500 VA / 360.256 = 145.73 A. The closest option is 144.2 A. There must be some rounding in the options or the question's intended answer. Let's use 144.2 A as the target, then recalculate. If current is 144.2 A, then total VA = 144.2 A * 208V * 1.732 = 51999.5 VA ≈ 52,000 VA. If lighting is 30,000 VA * 1.25 = 37,500 VA. This means the receptacle load would have to be 52,000 VA - 37,500 VA = 14,500 VA. Since the problem states 15,000 VA for receptacles, there's a slight mismatch. However, 144.2 A is the closest option by far to 145.73 A. Let's take the provided answer (A) as correct and work backwards. If 144.2 A is the answer, then total VA = 144.2 A * 208V * √3 = 51999 VA. This is roughly 52,000 VA. If lighting is 30,000 VA * 1.25 = 37,500 VA. Then the remaining VA for receptacles would be 52,000 VA - 37,500 VA = 14,500 VA. The question states 15,000 VA for receptacles. The difference is 500 VA. This is likely due to rounding in the option. 145.73 A (calculated) is closest to 144.2 A. The explanation will state the calculation that yields 145.73 A and point to 144.2 A as the closest option. Final calculation for explanation: 1. General lighting is usually considered a continuous load in commercial buildings. Therefore, its demand load is 125% of the connected load: 30,000 VA * 1.25 = 37,500 VA. 2. The receptacle load is given as 15,000 VA. We assume this is already the demand-factored value or a non-continuous load taken at face value. 3. Total demand VA = 37,500 VA (lighting) + 15,000 VA (receptacles) = 52,500 VA. 4. For a three-phase system, current (I) = VA / (V_line_to_line * √3). I = 52,500 VA / (208V * 1.732) = 52,500 VA / 360.256 ≈ 145.73 A. Of the given options, 144.2 A is the closest value.