A commercial building's electrical schedule shows a 200-amp, 3-phase panel. If the voltage is 208V, what is the maximum theoretical power capacity in kW?
Correct Answer
B) 72.1 kW
For 3-phase power: P = √3 × V × I ÷ 1000. P = 1.732 × 208V × 200A ÷ 1000 = 72.1 kW. This represents the maximum theoretical capacity of the electrical panel.
Why This Is the Correct Answer
Option B is correct because it uses the proper 3-phase power formula: P = √3 × V × I ÷ 1000. The square root of 3 (1.732) is the key factor that accounts for the phase relationships in 3-phase systems. This formula calculates the total power across all three phases, giving us the maximum theoretical capacity of 72.1 kW. This is the standard electrical engineering formula used for 3-phase power calculations in commercial applications.
Why the Other Options Are Wrong
Option A: 41.6 kW
This answer likely used single-phase calculation (P = V × I ÷ 1000 = 208 × 200 ÷ 1000 = 41.6 kW) instead of the correct 3-phase formula, missing the √3 multiplier factor.
Option C: 124.8 kW
This answer appears to have used an incorrect multiplier or formula, possibly confusing line-to-line voltage relationships or using 3 instead of √3 (1.732) in the calculation.
Option D: 208.0 kW
This answer simply multiplied voltage times current without any power conversion or proper formula application, ignoring both the 3-phase factor and the conversion to kilowatts.
Memory Technique
Remember 'Square root of THREE for THREE-phase' and the mnemonic 'Pretty Valuable Information' for P = √3 × V × I, then divide by 1000 for kW conversion.
Reference Hint
NEC Article 220 - Branch-Circuit, Feeder, and Service Load Calculations, or electrical engineering reference sections covering 3-phase power calculations
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