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Solved exercise · level 4 of 5

Correcting the cos φ of a motor

Skills: Calculate

Statement

A single-phase motor draws 3 A at 220 V, 50 Hz. Its useful power is 400 W with an efficiency of 0.8. What is its cos φ and what capacitor must be connected across it to raise cos φ to 0.9?

Motor power factor cos φ = P / S.

Parametric exercise: the values change with every draw; these are one example.

1 hint from Bastaya available in the lab
Solution

P = Pu / η = 500 W; S = U·I = 660 VA; cos φ = 0.758; Q = √(S² − P²) = 431 var; for cos φ′ = 0.9, Q′ = P · tan φ′ = 242 var; Q_C = Q − Q′ = 189 var; C = Q_C / (U²·ω) = 12.4 µF.

Course sheet of the chapter : AC power

This chapter is covered by the paths: General electricity, ISL-oriented exercises

Other exercises of the chapter

Simulated time00:00:00
Q = I·t-
W = P·t-

Circuit diagram CEI 60617

How does it work?

Each big hole is a circuit node: you push one leg of a component into it. The 4 small holes around it are connected to it: chips and leads plug in there.

  1. Place a component Drag it from the palette: it snaps onto the grid. R rotates it.
  2. Bridge neighbouring holes Pick the jumper chip (or C) and drag on the board: bridged holes become a single node.
  3. Draw a lead For long links and the power supply: from one big hole to another, or to a terminal.
  4. Close the loop The circuit is solved live (Ohm, Kirchhoff) and the diagram follows.

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