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
  

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.