Electrical Calculations Practice Test

For conductors smaller than 2 AWG the resistance comes from the K-factor: R = 12.9 x 1000 / 10,380 = 1.243 ohm per 1000 ft. Single-phase VD = 2 x 1.243 x 24 x 150 / 1000 = 8.9 V, about 3.7% of 240 V. The single-phase multiplier is 2 (out and back), not the sqrt(3) used for three-phase.

NEC Chapter 9, Table 8 (10,380 cmil for 10 AWG); single-phase VD = 2 x K x I x L / cmil

VD = 1.732 x 0.12 x 100 x 250 / 1000 = 5.2 V, about 2.5% of 208 V. Substituting the single-phase multiplier 2 for sqrt(3) overstates the drop to 6.0 V. For 1/0 AWG and larger this project reads Table 9 AC resistance directly rather than the K-factor.

NEC Chapter 9, Table 9 (0.12 ohm/1000 ft for 1/0 Cu in PVC); three-phase VD = sqrt(3) x R x I x L / 1000

R = 12.9 x 1000 / 6,530 = 1.975 ohm per 1000 ft. VD = 2 x 1.975 x 16 x 100 / 1000 = 6.32 V, and 6.32 / 120 = 5.3%. That exceeds the 5% combined feeder-plus-branch recommendation, so the conductor should be increased. The 3% and 5% figures are Informational Note recommendations, not mandatory limits.

NEC Chapter 9, Table 8 (6,530 cmil for 12 AWG); 210.19(A) Informational Note (3% branch-circuit recommendation)

Total conductor area = 9 x 0.0366 = 0.329 in². For more than two conductors Table 1 allows 40% fill. 3/4 in EMT (0.533 in² x 0.40 = 0.213 in²) is too small; 1 in EMT (0.864 in² x 0.40 = 0.346 in²) exceeds 0.329 in², so 1 in is the minimum trade size.

NEC Chapter 9, Table 1 (40% for 3 or more conductors), Table 4 (EMT internal area), Table 5 (THHN area)

Table 1 sets the fill limit by conductor count: 53% for one conductor, 31% for two, and 40% for three or more. A short nipple no longer than 24 in is permitted 60% fill under Chapter 9, Notes to Tables, Note 4. The 40% value governs the great majority of raceway pulls.

NEC Chapter 9, Table 1

Conductors: 6 x 2.00 = 12.00 in³. Clamp fill: one allowance = 2.00 in³ (B)(2). Device yoke: 2 x 2.00 = 4.00 in³ (B)(4), a double allowance. Equipment grounding conductors: one allowance = 2.00 in³ (B)(5). Total = 12 + 2 + 4 + 2 = 20 in³. Each allowance is based on the largest conductor in the box (here 14 AWG).

NEC Table 314.16(B); 314.16(B)(1) conductors, (B)(2) clamps, (B)(4) device yoke, (B)(5) grounding conductors

Start from the 90°C column: 8 AWG copper = 55 A. Six current-carrying conductors apply the 0.80 adjustment (Table 310.15(C)(1)): 55 x 0.80 = 44 A. The 75°C termination cap (110.14(C)) is 50 A, and since 44 A is below it, the adjusted 44 A governs the usable ampacity.

NEC Table 310.16 (90°C base 55 A), Table 310.15(C)(1) (0.80 for 4-6 conductors), 110.14(C) termination limit

The 43°C ambient falls in the 41-45°C row of Table 310.15(B)(1); the 75°C correction factor is 0.82. 85 x 0.82 = 69.7 A. NEC applies the factor for the range that contains the ambient, not a value interpolated at the exact temperature. With only three conductors no further adjustment applies.

NEC Table 310.16 (75°C base 85 A), Table 310.15(B)(1) (0.82 correction for the 41-45°C range at 75°C)

Table 310.16 lists 180 A for 4/0 aluminum in the 75°C column. 205 A is the 250 kcmil aluminum value and 230 A is the 4/0 copper value at 75°C, both common distractors. The 75°C column governs most terminations under 110.14(C).

NEC Table 310.16, aluminum 75°C column

With 75°C terminations the conductor is chosen from the 75°C column. 8 AWG copper is 50 A (below 60 A); 6 AWG copper is 65 A, which meets the 60 A load. So 6 AWG is the minimum. No small-conductor 240.4(D) cap applies at 6 AWG.

NEC Table 310.16 (75°C column), 110.14(C) termination limit

A continuous load requires the OCPD to be at least 125% of the load: 44 x 1.25 = 55 A. 55 A is not a standard 240.6(A) rating, so the next standard rating up, 60 A, is used. 55 A is the computed value, not a selectable device.

NEC 210.20(A) (125% of a continuous load), 240.6(A) standard ratings

80 A x 1.25 = 100 A. 100 A is a standard 240.6(A) rating, so a 100 A fuse is the minimum. Fuses use the same 240.6(A) standard ratings as breakers and additionally include 1, 3, 6, 10, and 601 A.

NEC 210.20(A) (125% of a continuous load), 240.6(A) standard ratings

Table 250.122 lists a 6 AWG copper equipment grounding conductor for overcurrent devices not exceeding 200 A. A 100 A device would need 8 AWG and a 300 A device 4 AWG. The table is indexed on the OCPD rating, not on the conductor ampacity.

NEC Table 250.122

Table 250.66: service conductors of 2/0 or 3/0 AWG copper require a 4 AWG copper grounding electrode conductor. Where the grounding electrode conductor connects only to a rod, pipe, or plate electrode it need not exceed 6 AWG (250.66(A)); to a concrete-encased electrode, 4 AWG (250.66(B)).

NEC Table 250.66

Primary rated current = 30,000 / (1.732 x 480) = 36.1 A. That is 9 A or more, so the primary-only device is limited to 125%: 36.1 x 1.25 = 45.1 A. 45.1 A exceeds the standard 45 A rating, so Note 1 permits the next higher standard 240.6(A) rating, 50 A.

NEC Table 450.3(B), primary-only 125% row with Note 1; 240.6(A)

Column C gives 8 kW for one range not over 12 kW. Note 1 adds 5% to the Column C value for each full kW the rating exceeds 12 kW: 14 - 12 = 2 kW, so 2 x 5% = 10%. 8 kW x 1.10 = 8.8 kW.

NEC Table 220.55, Column C, Note 1

220.82(B) takes 100% of the first 10 kVA and 40% of the remainder: 10 + 0.40 x (30 - 10) = 10 + 8 = 18 kVA. The larger of the heating or air-conditioning load from 220.82(C) is then added. The method usually yields a smaller service than the standard Article 220 Part III calculation.

NEC 220.82(B)

240.4(D) caps overcurrent protection for 12 AWG copper at 20 A regardless of ampacity (14 AWG copper at 15 A, 10 AWG copper at 30 A). This is an overcurrent-device limit, not an ampacity, and it overrides the higher 90°C table value when 12 AWG THHN is used.

NEC 240.4(D)

Both the overcurrent device (210.20(A)/215.3) and the conductors (210.19(A)(1)/215.2(A)(1)) are sized at 100% of the noncontinuous load plus 125% of the continuous load. The 125% factor is the inverse of the 80% continuous-loading limit on a standard-rated device.

NEC 210.20(A) and 210.19(A)(1) (branch circuits); 215.2(A)(1) and 215.3 (feeders)

250.66(A) caps the grounding electrode conductor to a rod, pipe, or plate electrode at 6 AWG copper (4 AWG aluminum), no matter how large Table 250.66 would otherwise require. 250.66(B) similarly caps the conductor to a concrete-encased electrode at 4 AWG copper. Both caps only ever make the conductor smaller.

NEC 250.66(A)