Parallel RLC circuits

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[/fusion_code][fullwidth backgroundcolor=”” backgroundimage=”” backgroundrepeat=”no-repeat” backgroundposition=”left top” backgroundattachment=”scroll” video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” bordersize=”0px” bordercolor=”” borderstyle=”” paddingtop=”20px” paddingbottom=”20px” paddingleft=”0px” paddingright=”0px” menu_anchor=”” equal_height_columns=”no” hundred_percent=”no” class=”” id=””][title size=”1″ content_align=”left” style_type=”single” sep_color=”” class=”” id=””]Why Power is your very best friend in a parallel RLC circuit.[/title][youtube id=”8tLhqs9gZdc” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][fusion_text]

Impedance is a bully

When dealing with a series circuit the only way to figure it out was to solve the impedance triangle.

From there you could get the current and the whole circuit would be unlocked.

That is only true for a series circuit.

Why is parallel any different?

When we add up resistors in parallel, we have to do it reciprocally.  The same holds true when adding reactance.

The issue is that they are all out of phase as well.  Therefore you have to add them up reciprocally as well as vectorially.

WTF???

Exactly.  So in the interest of not confusing the fuzzuck out of you I am not even going to touch on it.

Current will let you down

 In a series circuit we built voltage triangles.

In a parallel circuit that is not possible as voltage is now the new constant.

Does this mean we can build current triangles?

Yes and No.

The only time we can get away with building a current triangle (reliably) is when each branch is pure:

RLC, Parallel, current

Once you add a resistance to the inductive branch things get a little tricksy.  All the currents get out of phase.

Coil, parallel

Can you still figure it out using currents?  Sure but you are having to do it all vectorially and it becomes a royal pain in the ass.

Power is my friend!

 For some of you power may be the only friend you ever have.

You will always be given enough information to figure out the resistive and reactive powers.

Figure out the resistive and reactive powers through each branch (I draw a triangle under each branch).

parallel, triangles

Then you can go ahead and build one triangle to rule them all (Sorry for the cheesy Lord of the rings reference).  Add all your watts together in each branch.  Add all your Vars in each branch.

You can do this because vectorially they are heading the same direction.

Once you do this you have an overall power triangle.  Use the VA to determine the I line.

Use the I line and the source voltage to determine the circuit impedance.

Does this work every time?

Yup!  Even if your branches are all pure and there is no way to build a triangle for each branch.

power, triangle, parallel, rlc

Calculate your watts.

Calculate your VarsL.

Calculate your VarsC.

Determine Net Vars (VarsL – VarsC).

Then build your one triangle to rule them all.

 A parting thought.

Parallel RLC circuits can be as complex as you want them to be.  The thing is they don’t have to be.

Break everything down to power and you’ll be fine.

I have been teaching these circuits for years and it can always be brought back to power.

You’re welcome.

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