How can capacitive reactance be zero for no capacitor?

[bobaustin]

I have a quick question about a problem requiring calculating impedance of a circuit where there is no capacitor. The formula for impedance Z is
Z=sqrt(R^2 + (Xl - Xc)^2).
I am told capacitive reactance Xc = 0 because C = 0 (there is no capacitor in the circuit). But the formula for Xc is Xc = 1/2(pi)fC. So if C = 0, then Xc must be huge or infinite, not zero!
I'm confused. Can someone please explain this contradiction to me. Thank you!

P.S.: Maybe I should visualize replacing the nonexistent capacitor with a "short". A short has infinite capacitance, right?

 

[LowlyPion]

Welcome to PF.

Capacitance of 0 is like an infinite insulator right? An open circuit. No current flows.

If Xc is ∞, then no current flows for any ω.

 

[Phrak]

Th impedance Z is a complex value. Z = R + jX

 

[bobaustin]

Thanks for the insight. I was thinking C varies inversely with the capacitor gap d, so if there is no capacitor, then there is no gap, d goes to zero, which means C is infinite... Is this goofy thinking?

 

[fleem]

You give the formula for reactance in a series circuit.

The term "no capacitor" would typically be interpreted to mean a short in a series circuit and an open in a parallel circuit. So i think its meant that there is no capacitor in the series circuit.

The statement "capacitive reactance Xc = 0 because C = 0" is certainly flawed (i.e. not true in the general sense!). I suspect it should have been "capacitive reactance Xc = 0 because there is no capacitor in this series circuit".

Finally, yes, a short can be thought of as having infinite capacitance, but I wouldn't say that in front of a class since it would make the students think they have to look at wires as devices of infinite capacitance, resulting in long queues outside the instructor's office after the class.