# Parallel RLC Admittance, Current and Power Vector Diagrams

• pvshackguy
In summary, the conversation discusses the use of phasor diagrams and complex numbers in analyzing an ideal parallel RLC circuit. The experts suggest that a mathematical approach is the best way to communicate and that shorthand terminology can be confusing if one does not understand the rigorous approach behind it. They also mention the use of triangles to represent impedance, voltage, and power, and discuss the concept of sourcing and sinking VARs in relation to inductive and capacitive reactances. The original poster is seeking clarification on the use of complex math in teaching AC circuit analysis to electrician apprentices.
pvshackguy
(An even longer-winded version was written and deleted out of mercy.)

Assume an AC voltage at zero degrees applied to an ideal parallel RLC circuit.

For a predominantly inductive circuit, the vector diagram for current should show the supply current in the fourth quadrant (i.e. with lagging phase angle). Reduced to a triangle representation, it would be "hanging down" from the horizontal.

Now if I wanted to draw corresponding triangles for the circuit admittance and power, what would their orientations be? I have a guess but I'm not keen to embarrass myself in such company. (I really wish I hadn't just shipped my forty-year-old notes and textbooks ahead of me in advance of a move.)

Follow-up question: while digging through the net on this subject with mixed results, I ran across reference to reactances "sinking or sourcing VARs." I don't ever recall using these terms. I understand the opposite phase relationship yielding net reactive power, but sink vs. source?

pvshackguy said:
Follow-up question: while digging through the net on this subject with mixed results, I ran across reference to reactances "sinking or sourcing VARs." I don't ever recall using these terms. I understand the opposite phase relationship yielding net reactive power, but sink vs. source?
VAR stands for volt amp reactive. It is the imaginary component of complex power. It is a matter of sign convention that reactance consumes VARs. If that's so, then a capacitor must do the opposite and generate VARs. Consume is to generate as sink is to source.

But that jargon is not important. Can you solve that circuit with complex numbers rather than phasor diagrams? That is the easiest way to get the answers you seek.

berkeman
anorlunda said:
Can you solve that circuit with complex numbers
Yes, this!

Much of what you are asking is confusing to me because of nomenclature, although I do completely understand these circuits. A mathematical approach is the best way to communicate in these cases. Phasors are useful, but often applied by people that don't (yet) understand the fundamental behavior of the circuit. In those cases I think they add to confusion. Shorthand is great, but only if you know the more rigorous approach that they refer to.

Have you worked with the complex representation of impedance and how that relates to the amplitude and phase shift of the circuit responses (voltage, current, etc.)? This will help us know how to answer your question.
pvshackguy said:
Now if I wanted to draw corresponding triangles for the circuit admittance and power, what would their orientations be?
Sorry, I don't know what those triangles are. Yet, again, I do know about how these circuits behave.

pvshackguy said:
I ran across reference to reactances "sinking or sourcing VARs." I don't ever recall using these terms.
Sorry again, I don't understand this, it must relate to some polarity definition. For example, if you have an ideal voltage source connected to an ideal capacitor, would the source be sourcing or sinking VAR? I really only understand sourcing and sinking in terms of the real power component. Maybe someone else can let us know.

anorlunda said:
VAR stands for volt amp reactive. It is the imaginary component of complex power. It is a matter of sign convention that reactance consumes VARs. If that's so, then a capacitor must do the opposite and generate VARs. Consume is to generate as sink is to source.

But that jargon is not important. Can you solve that circuit with complex numbers rather than phasor diagrams? That is the easiest way to get the answers you seek.
Thanks for the post.

I assume you meant that an inductive reactance is considered to consume reactive power, therefore a capacitor must generate it. Considering that they are both energy storage devices that, in the ideal, store and return all of their energy to the circuit, I still can't think of a satisfying justification for the source/sink terminology. But that's OK. You confirmed that it's unimportant jargon.

As to your question regarding complex math, that is exactly what I am trying to add into course material for beginner electricians (tradespeople) who have traditionally been taught AC circuit analysis exclusively with triangles. I got through series RLC showing how the triangles for impedance, voltage and power relate to and are developed from complex math and vector diagrams, and was happily following the same approach for parallel RLC when I had this moment of doubt as to whether my graphical story was going to be as clear as it was for the series case.

DaveE said:
Yes, this!

Much of what you are asking is confusing to me because of nomenclature, although I do completely understand these circuits. A mathematical approach is the best way to communicate in these cases. Phasors are useful, but often applied by people that don't (yet) understand the fundamental behavior of the circuit. In those cases I think they add to confusion. Shorthand is great, but only if you know the more rigorous approach that they refer to.

Have you worked with the complex representation of impedance and how that relates to the amplitude and phase shift of the circuit responses (voltage, current, etc.)? This will help us know how to answer your question.

Sorry, I don't know what those triangles are. Yet, again, I do know about how these circuits behave.Sorry again, I don't understand this, it must relate to some polarity definition. For example, if you have an ideal voltage source connected to an ideal capacitor, would the source be sourcing or sinking VAR? I really only understand sourcing and sinking in terms of the real power component. Maybe someone else can let us know.
Hopefully my response to anorlunda will shed a little light. I am trying to build an instructional bridge between complex math and the triangles that electrician apprentices learn to use for AC circuit analysis. You've not seen triangles derived from vector diagrams, e.g. for current with sides IS, IR, IX?

pvshackguy said:
You've not seen triangles derived from vector diagrams, e.g. for current with sides IS, IR, IX?
Nope, never heard of them. In the academic track (at least the ones I know) that's just not taught.
Honestly, I have serious doubts about teaching reactive circuits before complex numbers (and maybe the simplest differential equations). At my school we were learning about Laplace transforms at that stage. I don't think an RLC circuit is really understandable without DEs. But we are all biased by the way we learned things, I'm sure it's a useful tool, whatever it is.

berkeman
DaveE said:
Nope, never heard of them. In the academic track (at least the ones I know) that's just not taught.
Honestly, I have serious doubts about teaching reactive circuits before complex numbers (and maybe the simplest differential equations). At my school we were learning about Laplace transforms at that stage. I don't think an RLC circuit is really understandable without DEs. But we are all biased by the way we learned things, I'm sure it's a useful tool, whatever it is.
Ah well, we're talking about trade apprentices here, quite a different set of priorities.

Forty years ago I became an electronics technologist. Then, after a lifetime of adventures that wound up involving too much time sitting at a computer, I decided to move to a rural setting and become an electrician. Now I sometimes teach beginner apprentices on a contract basis.

I can't deny that electricians can get through their training without a clue about complex math per se. Just a bit of trig and a few triangles as visual aids will do the trick. However I have been working up to introducing complex math explicitly on my next contract because it kills me that the students are using the principles without even knowing it.

The lion's share of the average "sparky's" job is actually codes and installation methods - craft, as it were. The supply voltage is usually a given and all legal loads have nameplates that spell out their requirements. Consequently, theoretical training emphasizes magnitudes - the sort of thing you can read in the field with a portable multimeter. Phase really only enters the picture in the context of power factor. In residential work or even most light commercial work, that isn't even a thing.

Anyhow, appreciate the help. I'm more comfortable now about how to handle this. I watched a few Youtube vids to remind myself about why the complex conjugate of current is used to calculate complex power (when voltage is the reference), and also reinforced what I learned here about the sign of reactive power (and the terms source and sink in that context) being more convention than concern. Thanks for jumping in and don't lose sleep over the triangles - or if you're curious, just punch something like "impedance triangle" into a search engine and behold the many hits.

Happy trails

## 1. What is a Parallel RLC Circuit?

A Parallel RLC circuit is a type of electrical circuit that contains a resistor (R), inductor (L), and capacitor (C) connected in parallel. This means that the components share the same voltage, but the current through each component can vary.

## 2. What is Admittance in a Parallel RLC Circuit?

Admittance is the measure of how easily an electrical component can conduct an alternating current. In a Parallel RLC circuit, it is represented by the symbol Y and is the inverse of impedance (Z).

## 3. How do you draw a Current Vector Diagram for a Parallel RLC Circuit?

To draw a Current Vector Diagram for a Parallel RLC circuit, you first need to calculate the total current in the circuit using Ohm's Law. Then, draw a horizontal line representing the real part of the current and a vertical line representing the imaginary part. The hypotenuse of the resulting triangle will represent the total current, and the angle of the triangle will represent the phase difference between the voltage and current.

## 4. What is the Power Factor in a Parallel RLC Circuit?

The Power Factor in a Parallel RLC circuit is a measure of how efficiently the circuit uses electrical power. It is represented by the symbol cos(ϕ) and is calculated by dividing the real power (P) by the apparent power (S). A higher power factor indicates a more efficient use of power.

## 5. How do you determine the Power Factor in a Parallel RLC Circuit?

To determine the Power Factor in a Parallel RLC circuit, you first need to calculate the real power (P) and the apparent power (S). Then, divide P by S to get the Power Factor (cos(ϕ)). Alternatively, you can use a Power Factor Meter to directly measure the Power Factor in the circuit.

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