Farad (F)

Also called F, Coulomb per volt

The farad is the SI unit of capacitance, equal to one coulomb of stored charge per volt of potential difference. It is an enormous unit, which is why real capacitors are rated in microfarads and picofarads.

Nothing on a circuit board is rated in whole farads. The unit comes from the printed definition of capacitance,

C = \frac{Q}{\Delta V}, \qquad 1\ \text{F} = 1\ \text{C/V}

and both of those are awkward sizes already: a coulomb is a huge static charge and a volt is a small potential difference, so their ratio is oversized twice over.

How oversized is worth working out once. The sheet also prints $C = \kappa\varepsilon_0 A/d$ , with $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N} \cdot \text{m}^2)$ and $\kappa = 1.0$ for the air-filled capacitors the exam conventions assume. Reaching $C = 1$ F with plates $1.0$ mm apart would take

A = \frac{d}{\varepsilon_0} = \frac{1.0 \times 10^{-3}}{8.85 \times 10^{-12}} = 1.1 \times 10^8\ \text{m}^2

roughly $113$ square kilometres of plate. Hence microfarads, nanofarads and picofarads.

It measures the hardware, not the contents. A capacitor charged to $12$ V and the same capacitor charged to $3$ V have identical capacitance, because $Q$ and $\Delta V$ move together. The farads are set by plate area, gap and dielectric.

Two unit identities worth carrying: a farad is also a coulomb squared per joule, from $U_C = \tfrac{1}{2}Q\Delta V$ , and an ohm times a farad is a second, which is the check behind the RC time constant.

Farad appears on the AP Physics 2 and AP Physics C: Electricity and Magnetism unit-symbol tables.

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