# 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
```

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