I was thinking about analogous situations for resistance, capacitance and inductance. For example, impedance, series and parallel combinations, damped mechanical vs electromagnetic oscillators.
In an AC circuit, impedance of a resistor is simply its resistance $=R$, that for an inductor is its inductive reactance times the imaginary unit $=\jmath\omega L$ but that for a capacitor is its capacitive reactance times the imaginary unit $=\frac{-\jmath}{\omega C}$, i.e., it depends inversely on capacitance unlike the other two.
The previous point(as resistance and reactance are the real and the imaginary parts respectively of impedance) leads to the fact that capacitances in parallel directly add up and in series, linear addition of reciprocal of capacitances takes place, which is opposite of what happens in series and parallel combinations of only inductors or only resistors.
The differential equation describing the motion of a damped mechanical oscillator is
$$m\frac{\mathrm d^2x}{\mathrm dt^2}+b\frac{\mathrm dx}{\mathrm dt}+kx=0$$
whereas for a damped series LCR circuit(electromagnetic oscillator), the differential equation describing the flow of charge in the circuit is $$L\frac{\mathrm d^2x}{\mathrm dt^2}+R\frac{\mathrm dx}{\mathrm dt}+\frac{q}C=0$$
which leads to the correspondences
$$m\leftrightarrow L$$ $$b\leftrightarrow R$$ $$k\leftrightarrow\frac1C$$
which is asymmetric due to the stiffness constant being analogous to inverse capacitance.
My question: Why is capacitance defined as $\frac{Q}V$ and not $\frac{V}Q$, as the aforementioned situations would have been symmetric for resistance, inductance and capacitance had $C=\frac{V}Q$?
