# Lead Lag in a resonant circuit?

Discussion in 'General Electronics Chat' started by electronice123, Jul 3, 2010.

1. ### electronice123 Thread Starter Senior Member

Oct 10, 2008
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In a series LC circuit at resonance the inductive and capacitive reactances equal to cancel each other out. Doesen't that mean that the voltage and current are in phase with no lead or lag?

Is there any way in which a series resonant LC circuit (operating at resonance) can have current which leads or lags the voltage?

Last edited: Jul 3, 2010

Apr 20, 2004
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3. ### steveb Senior Member

Jul 3, 2008
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It's easiest to think in terms of the phasor representation using complex impedances. To have a phase lead or lag, the impedance needs to be complex or imaginary, but as you pointed out it is real for an LC circuit at resonance.

So, you need to either modify the circuit so that it is not a simple series LC, or tune off the resonance peak. The bottom line is the effective impedance needs to have a nonzero imaginary component in order for current and voltage to not be in phase.

For a series RLC circuit, the impedance is:

$Z=R + X_L + X_C = R + {\rm j} \omega L+ {{1}\over{{\rm j} \omega C}}$

where j is the square root of negative one. Remember that j=-1/j which is what allows the inductive and capacitive reactances to cancel.

4. ### lmartinez Active Member

Mar 8, 2009
224
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j= -1/j not a truth statement.

5. ### steveb Senior Member

Jul 3, 2008
2,433
469
DEFINITION: j is a number which when multiplied by itself equals -1

Multiply one side by -1/(-1) which equals unity: j = j * (-1)/(-1)

Convert the -1 in the denominator to j*j using the definition of j: j = -j/(j*j)

Note that j/j equals unity since any number divided by itself is unity (excluding 0/0): j = -1/j

Hence, j = -1/j is a truth statement.

Last edited: Jul 4, 2010
6. ### Ron H AAC Fanatic!

Apr 14, 2005
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The simplest definition of j is (in my opinion).

$j=\sqrt{-1}$

7. ### steveb Senior Member

Jul 3, 2008
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What is the alternative? Not only is it the simplest definition, but I thought it was the only definition. I'd be interested to hear of any alternatives, if they exist.

8. ### lmartinez Active Member

Mar 8, 2009
224
6
I concur with the latter statement....Happy fourth of JULY..........

9. ### steveb Senior Member

Jul 3, 2008
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So, which "former statement" do you not concur with?

How are we helping the OP with these statements that seem to imply there is an unspoken issue?

The definition given is exactly the one I gave. I gave a two different verbal definitions that are identical to this one. The second one was given as a preferred wording to prove the identity I gave, and which you said was wrong.

The following responses seem to make a subtle implication that something is wrong. Even if this is not the intent, it is not helpful to the OP.

10. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
Sorry, Steve.
I took this:
out of context and read j = -j/(j*j) as being presented as the definition of j.
I reread the post and realized that the equation was the result of the mathematical manipulation you were performing to prove the "truth statement", which I do not and did not dispute.

11. ### steveb Senior Member

Jul 3, 2008
2,433
469
No problem Ron. Yeah, that would be a needlessly confusing definition.

I just want to make sure we aren't giving the OP the wrong message, that's all.