Commissioning a 3 kW grinder on a long final circuit
A trainee at a government ITI workshop in Nalbari has to commission a 3 kW, 230 V single-phase grain grinder at the far end of a shed. The machine is fed from the main switchboard by a 45 m run of 2.5 mm² two-core copper PVC cable clipped to the wall, protected by a 16 A MCB. At no load the board voltage is 236 V. With the grinder running, the voltage measured at the machine terminals is 212 V; the grinder turns slowly, its body smells hot, and the cable near the switchboard is noticeably warm. The MCB has tripped twice in a week, and the shopkeeper's helper suggests fitting a 32 A MCB 'so it stops tripping'. Ambient temperature is 35 °C and the run passes through about 6 m of hot roof space. Take copper resistivity as 0.0173 Ω·mm²/m and treat the grinder as unity power factor for this exercise.
1. Calculate the full-load current and the voltage drop that the cable alone should produce. Compare this with the measured drop and say what the difference proves.
Read the worked answer
Load current. I = P/V = 3000/230 ≈ 13.0 A. (A capacitor-run motor draws a little more than this because of magnetising current, never less.)
Drop the cable can explain. Resistance per conductor = ρL/A = 0.0173 × 45 / 2.5 = 0.311 Ω. Current travels out and back, so the loop resistance is 2 × 0.311 = 0.623 Ω. ΔV = I × R_loop = 13.0 × 0.623 ≈ 8.1 V, i.e. about 3.4% of 236 V - inside the 5% (11.5 V) figure normally applied to a final circuit.
Measured drop. 236 − 212 = 24 V, about 10.2%.
What the gap proves. The cable's distributed resistance accounts for roughly one-third of the measured drop. The remaining ~16 V corresponds to about 1.2 Ω concentrated somewhere in the circuit. A lump of that size is almost never cable - it is a series fault: a loose terminal screw, a taped twist joint, a corroded lug, a partly cut conductor, or a worn switch contact. Distributed cable resistance would give a gentle, predictable drop; a hot spot near the board plus an unexpectedly large drop points to contact heating.
Before blaming the joint, clamp the actual running current. If the grinder is mechanically overloaded or the start capacitor is failing, the true current may be well above 13 A and the arithmetic shifts - but the extra ~1.2 Ω will not vanish, so a high-resistance point is still the prime suspect. Also remember the 6 m roof-space section: at 35 °C ambient it is derated, so the warmth there is a separate loading symptom.
2. The helper wants a 32 A MCB fitted. Evaluate that proposal and state what the protective device is actually protecting.
Read the worked answer
Refuse it. The MCB protects the cable, not the appliance. Its job is to disconnect before the conductor insulation is damaged.
Capacity of the cable. A 2.5 mm² copper PVC two-core cable clipped direct is good for roughly 24 A at 30 °C. Apply about 0.94 for 35 °C ambient, and a further factor for the roof-space section where the cable is grouped and hot - a realistic derated capacity is nearer 18–20 A.
Consequence of a 32 A device. It would sit well above the cable's derated capacity, so a sustained 25–30 A could flow through a conductor rated for about 18 A without ever tripping. The result is gradual insulation carbonisation, then a short circuit or fire inside the roof space - exactly where nobody is watching. The 32 A device also does nothing about the contact heating that is causing the present drop.
Why the 16 A is tripping at only 13 A nameplate. Either the real current exceeds 16 A (mechanical overload, failing capacitor, dragging bearing) or the MCB itself is weak or the terminal is loose and heating it. Both must be measured, not guessed.
Correct action. Keep the protection matched to the conductor, cure the high-resistance point, and if the run genuinely needs more current-carrying capacity, upgrade the cable and the device together - never the device alone.
3. Set out the sequence of tests you would carry out before and after re-energising, and calculate the cable size that the run really needs.
Read the worked answer
Safe sequence.
- Isolate, lock off, prove dead at the machine terminals, and discharge the motor capacitor.
- Clamp the true RMS running current on the live conductor with the machine under its normal mechanical load.
- With the supply off, measure end-to-end resistance of each core with a micro-ohmmeter or low-reading continuity tester, and flex the cable at suspected points - a resistance that changes when flexed is a broken strand.
- Inspect and re-terminate every joint and terminal with correct lugs and the specified torque; replace any taped twist.
- Insulation resistance at 500 V DC, phase-to-neutral and phase-to-earth: expect 1 MΩ or more.
- On re-energising, re-measure terminal voltage under load and check the cable surface temperature after 30 minutes.
Sizing calculation. For a 3% drop (6.9 V of 230 V): A = 2ρLI/ΔV = (2 × 0.0173 × 45 × 13.0) / 6.9 = 20.24 / 6.9 ≈ 2.9 mm² → use 4 mm².
At the 5% limit (11.5 V) the arithmetic gives only about 1.8 mm², so 2.5 mm² would pass on drop alone - but it leaves no margin once the 35 °C ambient and the hot roof section are applied. 4 mm² is the sound engineering choice, and the roof section should be re-routed or protected so that the derating factor is less severe.