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Series Resonant Circuit

For the series R-L-C circuit resonance will occur when the total impedance is purely resistance.

This occurs when XL = XC...

With this We Can Expand This

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia  and gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

 or gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia where  gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(1)
 and gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (2)

We Already Know, From the Earlier Discussions, that

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia and gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia and gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

And We Allow H to be a Multiple of "F," We Can Force (2) to Look Like this

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia then changing this to

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia


Reducing this We Get

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(3)

H will be the harmonic multiple to the fundamental.

From an Earlier Paper We Showed the Following

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

From (3) We Can Come Up with the Systems Harmonic Resonance

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(4)

Where

H = harmonic order...

MVAsc gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = available short circuit at the capacitor bank.

MVAR = capacitor bank size.
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