Amateur Extra: LC Current at Resonance

This week’s Amateur Extra question is from sub-element 5 (Electrical Principles) group A (characteristics of resonant circuits) [E5A06]

What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance?

A. It is at a minimum
B. It is at a maximum
C. It equals 1 divided by the quantity 2 times Pi, multiplied by the square root of inductance L multiplied by capacitance C
D. It equals 2 multiplied by Pi, multiplied by frequency “F”, multiplied by inductance “L”

OK, buckle down, kids, because here we go.  Time to roll up those sleeves and dive into some electrical math junk.  I know, I know, but when we’re done, it will make sense.  I hope.

The answer is B) It is at a maximum.  We’ll explain here.

The current in a parallel RLC circuit is the sum of the current in each section, or branch.  We’ll call them IL and IC.  Remember those equations for reactance, because we’ll use them here.  (as XL and XC.)

IL = V/XL = V/2{\pi}fL and IC = VXC = 2{\pi}VfC

if we sum these “vectors” together (remember the complex aspect of these!) we get

I = \sqrt{(IL + IC)}

at resonance, the currents in the capacitor and inductor are equal, but 180º out of phase, so they cancel each other out….

…. BUT ….  What we’ve just described it that the current leaving the circuit is zero.   How can the answer be “at a maximum?”

Another term for a parallel LC circuit is a “tank circuit.”  If you take this figuratively, consider this circuit as a tank of water, and the current the flow of water.  If the water going in doesn’t also come out, it has to go somewhere.  Where? Into the “tank.”

Remember above that the two vectors canceled each other out?  The effect on the AC current is the same.  The C current is going one way, and the L is going the other, so it cancels out.  You can even think of this as two halves of a loop, hence the term “circulating” current.  All the current goes in and just keeps turning around in circles, never leaving.

I know, I know, its a little weird.  But that’s how it is.  All the current gets stuck in the LC circuit and never leaves.  So the “circulating current within the components” is at a maximum.

Any questions? Good, because I’m not even sure I understood that completely now!!

In practical use, an example of a “tank circuit” might be the notch filter on your radio transceiver, it will block signals of a particular frequency from passing through the circuit.

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