Capacitors and RC Circuits

When capacitors are arranged in parallel, the equivalent capacitance is
```
               Ceq = C1 + C2 + C3 + ...
```

When capacitors are arranged in series, the equivalent capacitance is

                1     1     1     1
               --- = --- + --- + --- + ...
               Ceq    C1    C2    C3

Combining capacitors and resistors together in a circuit produces a time-varying current. The timescale over which the current (or charge on the capacitor, or voltage across the capacitor) changes is
```
             time constant = R * C            (seconds)
```
Quantities in an RC circuit change exponentially, which means quickly at first, then more and more slowly. Values change by the same multiplicative factor (such as 1/2) in every equal step of time.

As one charges a capacitor in an RC circuit,

                                               -t/RC
             charge on capacitor = Co * ( 1 - e      )

                                         -t/RC
             current in circuit  = Io * e

As one discharges a capacitor in an RC circuit,

                                         -t/RC
             charge on capacitor = Co * e

                                         -t/RC
             current in circuit  = Io * e