# Solving reactive circuits

#### CosPhi

Joined Mar 5, 2014
4
I'm new to AC circuits and i'm learning how to solve them.
Are reactances very much equivalent to resistance? Suppose if I have two inductors in series, can I add their reactances? Or, should I take the square root of the sum of their squares (like impedance)? Is it the same for two capacitors?
Thanks for any help in making me understand!

#### MrChips

Joined Oct 2, 2009
28,155
I have move your post from "General Electronics Chat" to "Physics".

#### MrChips

Joined Oct 2, 2009
28,155
• rc3po

#### #12

Joined Nov 30, 2010
18,224
One component at a time, you can kind of think of them as resistors, except the resistance changes with frequency. As soon as you get 2 different parts involved, you get into the "squared" equations.

#### CosPhi

Joined Mar 5, 2014
4
Thank you very much. I understand now.
Is there any equivalent of Kirchoff's laws applicable to reactances? I know that in reactive circuits the sum of squares of potentials is considered. Is the voltage across the resistor also treated that way?

#### WBahn

Joined Mar 31, 2012
28,192
I think you are being too quick to throw equations at things instead of understanding them first.

You want to keep resorting to some "sum of squares" equation for everything. As MrChips said, take a step back and understand what reactance and impedance are.

Do you know what complex numbers are and how to work with them? If so, then that makes like a lot easier because we can use the complex representation for these things and let the math take care of the bookkeeping for us. The reason that complex numbers are used is because inductors and capacitors have a 90 degree phase shift between the voltage across them and the current through them. Similarly, imaginary numbers are rotated 90 degrees relative to real numbers on a 2-D plot. So we can represent inductors and capacitors using imaginary numbers and resistors using real numbers and the trigonometry between them matches the interplay of the phase angles in the components.

You don't HAVE to use complex numbers, but it sure makes like easier.

#### CosPhi

Joined Mar 5, 2014
4
I know to work with complex numbers a bit. I don't have a strong hold on it. That's why I asked for equations. Just to be straight, I really don't know to work with them.
The problem is I want know how to solve for, for example a current in the branch of a series-parallel combination of reactive elements, or power dissipated in one of the resistances, so after understanding resistances and reactances, how should I go on to solving networks on them? Should I use phasors? Sorry if I sound dumb.
Thanks.

#### WBahn

Joined Mar 31, 2012
28,192
I know to work with complex numbers a bit. I don't have a strong hold on it. That's why I asked for equations. Just to be straight, I really don't know to work with them.
The problem is I want know how to solve for, for example a current in the branch of a series-parallel combination of reactive elements, or power dissipated in one of the resistances, so after understanding resistances and reactances, how should I go on to solving networks on them? Should I use phasors? Sorry if I sound dumb.
Thanks.
What you should do depends on what you are trying to do.

Here's what I mean. If you are trying to find the response of the circuit to a sinusoidal steady state signal, then you can use phasors. But if you are trying to solve for the transient response of the circuit, you can't use phasors because the phasors only let you solve for the sinusoidal steady state response.

Let's take a step back. How comfortably are you with using the standard techniques to solve arbitrary resistive circuits? Are you comfortable with solving circuits using KVL, KCL, node voltage qnalysis, mesh current analysis, Thevenin/Norton equivalent circuits, and superposition?

If not, go back and strengthen you abilities with those techniques. This is important because working with reactive components in steady state uses the exact same techniques, just with complex numbers. This makes things a bit more, well, complex; so it's best to have a good handle on the basics.

Do you have any background in calculus?

• rc3po

#### CosPhi

Joined Mar 5, 2014
4
Here's what I mean. If you are trying to find the response of the circuit to a sinusoidal steady state signal, then you can use phasors. But if you are trying to solve for the transient response of the circuit, you can't use phasors because the phasors only let you solve for the sinusoidal steady state response.
Ahh.. OK then.
Let's take a step back. How comfortably are you with using the standard techniques to solve arbitrary resistive circuits? Are you comfortable with solving circuits using KVL, KCL, node voltage qnalysis, mesh current analysis
Iam good at them. Not a super expert but I have solved them thoroughly and have a right hand at them.
Thevenin/Norton equivalent circuits, and superposition?
I know the thevenin/norton quite well and have worked with them (not as good as the KCL and KVL). But not superposition theorems.
Do you have any background in calculus?
Yes.