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Solved exercise · level 5 of 5

Cos φ of a coil in parallel with a resistor

Skills: Calculate

Statement

A coil (R₁ = 10 Ω, L = 50 mH) is connected in parallel with a resistor R₂ = 38 Ω across a 220 V, 50 Hz supply. Compute the cos φ of the circuit (power method: P and Q of each branch).

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

2 hints from Bastaya available in the lab
Solution

Coil: Z = 18.6 Ω, P₁ = R₁·U²/Z², Q₁ = Lω·U²/Z²; resistor: P₂ = U²/R₂, Q₂ = 0; P = 2670 W, Q = 2190 var; cos φ = P / √(P² + Q²) = 0.773; I = S / U = 15.7 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.

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