So ChatGPT gets it wrong again?You still have an impedance triangle except in the case where the inductive reactance is equal to the capacitive reactance. In that case you have a degenerate triangle along the real axis. This happens because of the presence of the imaginary unit j in the denominator of the expression for capacitive reactance.
\( \cfrac{1}{j\omega C}\cdot\cfrac{j}{j}\;=\;\cfrac{j}{j^2\omega C}\;=\;\cfrac{-j}{\omega C} \)
Taking the magnitude of the impedance to get the reactance, we get the desired expression:
\( X_{TOTAL}\;=\;X_L\;-\;X_C \)
I did not say that. In fact, I think they have it right. The two reactances do indeed have opposite signs. Just look at a VNA display.So ChatGPT gets it wrong again?
Yes - of course. ChatGPT did not consider any phase shift - the result will be a complex impedance.So ChatGPT gets it wrong again?
But you just said (correctly): "You still have an impedance triangle except in the case where the inductive reactance is equal to the capacitive reactance." ChatGPT didn't mention equal magnitudes. Am I missing something?I did not say that. In fact, I think they have it right. The two reactances do indeed have opposite signs. Just look at a VNA display.
Don't rely on ChatGPT to EVER be correct. Yes, sometimes it is, but only because it happens to statistically end up being the most likely chain of words in its search vector. The correctness, and internal consistency even, of that search vector depends on how predominant the "correct" answer is. As soon as you start adding in common alternate ways of expressing things, the quality of it's generated babble goes to hell.Hmmmm?....
Is ChatGPT correct here? If a series circuit containing a capacitor, inductor and resistor is driven at a known fixed frequency, then is the Impedance calculation as simple as Z=R+Xl-Xc? Why is the impedance triangle not necessary?
They only have it right under the very special case that the two reactances cancel each other out (i.e., at resonance). The response says nothing about resonance, only that the frequency is fixed. At anything other than resonance, their equation is simply wrong.I did not say that. In fact, I think they have it right. The two reactances do indeed have opposite signs. Just look at a VNA display.
I know you understand complex impedance. I was just reacting to this statement: " I think they have it right ".The only time you have a triangle is when the imaginary part is nonzero. When the imaginary part is zero and the real part is nonzero the triangle collapses into a line. If you are missing something, I can't fathom what it might be.
ETA: Reactances are real numbers, and the corresponding impedance is the reactance times the imaginary unit j. It is wrong to add a resistance and a reactance. The magnitude of a resistance and a non-zero net reactance is:
\( Z_T\;=\;\sqrt{R^2+X_T^2} \)
For normal frequency ranges where lumped components are appropriate, what they got right was the signs of the reactances. I glossed over the part about adding reactance to resistance. That is never appropriate.I know you understand complex impedance. I was just reacting to this statement: " I think they have it right ".
Thanks for the reply. I have found ChatGPT to be wrong in many instances, especially basic mathematics. I was pretty certain it was incorrect, but then I always question my own understanding.Don't rely on ChatGPT to EVER be correct. Yes, sometimes it is, but only because it happens to statistically end up being the most likely chain of words in its search vector. The correctness, and internal consistency even, of that search vector depends on how predominant the "correct" answer is. As soon as you start adding in common alternate ways of expressing things, the quality of it's generated babble goes to hell.
The impedance of a series circuit is the sum of the individual impedances. But impedances are complex quantities, while reactances are the real coefficients of impedance (and resistances are the real part of the impedance). Resistances add in series. Reactances add in series. Resistance and reactances in series do not add.
The ChatGPT response also makes a very common mistake (because this is an extremely common mistake found all over the place) and has capacitive reactance as being a positive quantity. It isn't, it's negative. But it is common for "trade school" level courses to treat it as a positive number and then deal with the fact that it is negative by mangling simple equations in order to artificially carrying the minus sign via subtraction. This works find for the simplest of cases, but it makes it extremely difficult to analyze more complex systems symbolically because you end up with exploding special cases based on whether the unknown magnitude of the inductive reactance is greater or less than the capacitive reactance, rather than just treating reactance as reactance and letting the math take care of itself in the end.
At least the ChatGPT response came with with a series of babble that turned out to be internally consistent in this sense, which is far from always being the case.
This is a very good attitude, which I have often missed, for example, in the discussion of how the bipolar transistor really works...... I always question my own understanding.
If I may be a little polemical: sometimes I get the impression that AI is often used by people who don't have enough NI (natural intelligence).Thanks for the reply. I have found ChatGPT to be wrong in many instances, especially basic mathematics. I was pretty certain it was incorrect, but then I always question my own understanding.
Hi,Hmmmm?....
Is ChatGPT correct here? If a series circuit containing a capacitor, inductor and resistor is driven at a known fixed frequency, then is the Impedance calculation as simple as Z=R+Xl-Xc? Why is the impedance triangle not necessary?
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