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Boss lesson · The Machine Room Final
Exam-hall rules, last machine
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Exam-hall rules, last machine

This is the boss. No calculator, and the numbers are chosen to fit in your head. One motor, four lines, and every answer feeds the next: field speed from the supply, slip from the strobe reading, input power from the efficiency, line current from the input power. Write each line down as you go — one early slip rolls all the way to the feeder.

The last line hides a pleasant accident worth knowing for life. A power factor of 0.866 is cos⁡30∘\cos 30^\circ, which is 32\dfrac{\sqrt{3}}{2} — so 3 V PF=3⋅32⋅V=1.5V\sqrt{3}\,V\,\mathrm{PF} = \sqrt{3}\cdot\dfrac{\sqrt{3}}{2}\cdot V = 1.5V exactly. At 400 V that is 600 watts per amp, and the whole three-phase calculation collapses into a division you can do standing at a starter panel.

Everything in the chapter rides in this one machine. 5★ under par here is the chapter crown. Clock in.

pfNs

Ns=2fpN_{s} = \frac{2f}{p}

  • NsN_{s}= Synchronous speed (frequency)
  • ff= Supply frequency (frequency)
  • pp= Number of poles
Synchronous Speed from Frequency and Poles solver →
NsNrs

s=100 (Ns−Nr)Nss = \frac{100 \, (N_{s} - N_{r})}{N_{s}}

  • ss= Slip (concentration)
  • NsN_{s}= Synchronous speed (frequency)
  • NrN_{r}= Rotor speed (frequency)
Induction Motor Slip solver →
MηPinPout

η=100 PoutPin\eta = \frac{100 \, P_{out}}{P_{in}}

  • η\eta= Efficiency (concentration)
  • PoutP_{out}= Output power (power)
  • PinP_{in}= Input power (power)
Motor Efficiency solver →
MηVIPoutPF

I=Pout3 V PF ηI = \frac{P_{out}}{\sqrt{3} \, V \, \text{PF} \, \eta}

  • II= Full-load line current (electric current)
  • PoutP_{out}= Shaft output power (power)
  • VV= Line-to-line voltage (voltage)
  • PF\text{PF}= Power factor
  • η\eta= Efficiency (concentration)
Three-Phase Motor Full-Load Current solver →
no calculator in the boss room — the numbers are chosen to fit in your head