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Unarmoured cable for 15 hp motor at 79 m

Short answer

Motor full-load current is 23.75 A; design current (125%) is 29.7 A. From the table, 4 mm² unarmoured copper cable rated 31 A is selected. Voltage drop is 11.57 V (2.89%), within 5%. Cable size: 4 mm².

A 3-phase 15 hp, 400V, 50 Hz induction motor is to be installed in a workshop. Assuming the efficiency of the motor to be 85% and power factor 0.8, calculate the size of the unarmoured copper cable to be used if the distance between SDB and motor is 79m.

Conductor area (sq.mm)1.52.54610162535507095120150
3.5 core cable current rating (A)21273145607799120145175210240270

Given: P_out = 15 hp, V = 400 V (3-phase), η = 85 %, pf = 0.8, length SDB → motor = 79 m.

Assumptions: 1 hp = 746 W; cable chosen for 125 % of motor full-load current (motor circuit rule of IS 732/NEC); Cu resistivity 0.0178 Ω·mm²/m; permissible voltage drop 5 % (20 V). Table ratings are used for the unarmoured multicore Cu cable.

Step 1: Full-load current

Output P_out = 15 × 746        = 11,190 W
Input  P_in  = 11190 / 0.85    = 13,164.7 W
I_FL = P_in / (√3 × V × pf)
     = 13164.7 / (√3 × 400 × 0.8)
     = 23.75 A

Step 2: Design current and cable from table

Design current = 1.25 × 23.75 = 29.69 A

From the table, the next rating above 29.69 A is 31 A → 4 mm².

Step 3: Voltage drop check

R  = ρL/A = 0.0178 × 79 / 4 = 0.3515 Ω
ΔV = √3 × I × R × cos φ
   = √3 × 23.75 × 0.3515 × 0.8 = 11.57 V
%ΔV = 11.57/400 × 100 = 2.89 %  (< 5 %, OK)

Answer: 4 mm² Cu unarmoured (3.5/4-core) cable — full-load current 23.75 A, voltage drop 11.57 V (2.89 %). Protect the motor with a 32 A TP MCB (D-curve) or MPCB and a thermal overload relay set at about 24 A.

✓ Answer checked by Claude Opus 5.5 (high effort)

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