Electronic – Finding the resistance of a practical inductor having its reactive power

inductorpowerpractical

Suppose I have a simple practical inductor as such:

schematic

simulate this circuit – Schematic created using CircuitLab

L is known. R is unknown and we need to find it. The supply frequency (say \$f\$) is known. Also the reactive power on the whole inductor (say \$Q_i\$) is known.

Here's my approach. The reactance on the inductive part would be (say \$\chi\$ )

$$\chi = \omega L$$

(where \$ \omega = 2*\pi*f\$). So the impedance triangle and the power triangle would be something like this:

The two triangles

that angle a is equivalent in both triangles. so this would mean that:

$$\frac{\chi}{R} = \frac{Q_i}{P_i}$$

We don't have \$P_i\$ …however I have a source that says that the equation is just

$$\frac{\chi}{R} = Q_i$$

and that we can get R. The source doesn't provide steps. Just the equation. What am I doing wrong??

Actually I need to solve (the first part) of a question. Here's a screenshot of the question and the part of the solution of concern.

for reference

Best Answer

Ther mistake you made was assuming Q meant "reactive power" - it doesn't it's the Q-factor of the coil and quite simply is \$X_L/R\$. Q-factor is something you should look up. Q is sometimes called quality factor. See this wiki page. It's embodied in an RLC resonant tuned circuit for instance by this formula: -

enter image description here

And, for just the inductor on its own is simply \$X_L/R\$

Related Topic