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Solved exercise · level 4 of 5

Heater and motor at a subscriber

Skills: Calculate

Statement

A subscriber has 220 V, 50 Hz. They use at the same time a 40 Ω heater and a single-phase motor drawing 3 A with cos φ = 0.8. What powers do a wattmeter and a varmeter near the meter show? What is the total current?

Total active power P = ΣP (wattmeter).

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

1 hint from Bastaya available in the lab
Solution

P₁ = U²/R = 1210 W; P₂ = U·I·cos φ = 528 W → P = 1740 W; Q = Q₂ = U·I·sin φ = 396 var; S = √(P² + Q²) = 1780 VA; I = S / U = 8.1 A.

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.

Shortcuts

Del
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R
rotate
C
chip brush
Esc
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drag background
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