In practice, capacitors deviate from the ideal capacitor equation in several aspects. Some of these, such as leakage current and parasitic effects are linear, or can be analyzed as nearly linear, and can be accounted for by adding virtual components to form an equivalent circuit. The usual methods of can then be applied. In other cases, such as with breakdown voltage, the effec.
In fact, that's exactly what you do. Capacitors are only short circuits when you consider the "small signal" component after you found the DC linearized point. So capacitors are open when considering the DC component, then shorts (or at least small negative imaginary impedance) when solving for the non-DC small signal response.
What does a short circuit mean in real life?
In "real life", a circuit diagram would not normally include a permanent wire connecting both ends of a capacitor. A short circuit here means that there is no resistance (impedance) between the two terminals of the shorted capacitor. The vertical wire drawn next to the vertical capacitor shorts the two terminals of the capacitor.
Are coupling capacitors a short circuit?
When you treat them as short circuits you are making the assumption the have negligible reactance at the frequencies you are interested in. This is usually true for the coupling capacitors in an amplifier circuit. There are also capacitors you treat as open circuits because they have very large reactance at the frequencies of interest.
The vertical wire drawn next to the vertical capacitor shorts the two terminals of the capacitor. Any current flowing through this circuit segment will flow through the vertical wire and completely bypass the vertical capacitor due to the short. This means you can ignore the shorted capacitor -- it has no effect on the circuit.
Why does a capacitor have a short terminal?
By having their shorted terminals, the voltage thereof is zero (more precisely, the potential difference between them), so that this element is not operational in the circuit, and can be removed for analysis. The other two capacitors are in series, hence that:
So momentarily, the capacitor acts as a short once you subtract its current DC value, just like an ideal voltage source would. Just how momentarily, depends on the capacitance and the current we are talking about. A DC current will not stop changing the voltage, so for DC currents we have no stable operating point.