Capacitance

Also called Capacitor

Capacitance is the charge stored on one plate of a capacitor divided by the potential difference between the plates, measured in farads. It is fixed by the geometry of the device and the material in the gap, so storing more charge does not change it.

Two words get swapped and should not be. A capacitor is the device: two separated conducting surfaces carrying equal and opposite charge. Capacitance is the property that device has, and it is the ratio the sheet prints:

C = \frac{Q}{\Delta V}

$Q$ is the magnitude of the charge on one plate, not the total over both, which is zero. The unit is the farad, one coulomb per volt, and a farad is enormous: practical capacitors are microfarads and picofarads.

The ratio is set by the hardware. Put more charge on the plates and the potential difference rises in exact proportion, leaving $C$ alone. For parallel plates,

C = \frac{\kappa \varepsilon_0 A}{d}

so capacitance depends on the area of one plate, the plate separation, and the dielectric constant of whatever fills the gap. Neither charge nor voltage appears. A question that charges a capacitor to twice the voltage and asks what happened to $C$ is testing exactly that.

The energy stored is $U_C = \frac{1}{2} Q \Delta V$ . AP Physics 2 restricts analysis to parallel-plate capacitors and ignores edge effects unless a question says otherwise, and the series and parallel combination rules are filed with RC circuits rather than with the device itself.

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