AC Components and Circuits Capacitance
Section 55 Total Capacitance The total capacitance of series and parallel capacitor circuits is found by using the same forms of equations that apply to resistor and inductor circuits. There is one very significant difference, however. See the diagrams and corresponding equations shown below. Capacitors in Series C_{T} =  1  1  +  1  +  1    C_{1}  C_{2}  C_{3}    Capacitors in Parallel C_{T} = C_{1} + C_{2} + C_{3}  Equations Total Capacitance of a Series Circuit C_{T} =  1  1  +  1  +  1  + ... +  1  C_{1}  C_{2}  C_{3}  C_{n}  Total Capacitance of a Parallel Circuit C_{T} = C_{1} + C_{2} + C_{3} + ... + C_{n} Where  C_{T} = Total capacitance of the series circuit
 C_{1}, C_{2}, C_{3}, C_{n} = Values of all the individual capacitors
 IMPORTANT The equations for total capacitance for series circuits uses the equation of a form for parallelconnected resistors and inductors. Likewise, the equation for parallelconnected capacitors has the same form as the equation for seriesconnected resistors and inductors.  The productoversum technique that is commonly used for pairs of parallel resistors works equally well for pairs of series capacitors. C_{T} =  C_{1}C_{2}   C_{1} + C_{2}  The shorthand notation for this equation is also to the parallelresistance counterpart: C_{T} = C_{1}  C_{2} Example Problem Use the productoversum equation to find the total capacitance of a series circuit comprised of capacitors having values of 12mF and 48mF. Procedure 1. Cite the appropriate equation: C_{T} =  C_{1}C_{2}   C_{1} + C_{2}  2. Substitute the given values C_{T} =  (12 x 10^{6})(48 x 10^{6})   (12 x 10^{6}) + (48 x 10^{6}  3. Do the math  (12 x 10^{6})(48 x 10^{6})  = 9.6 x 10^{6}  (12 x 10^{6}) + (48 x 10^{6})  Solution C_{T} = 9.6mF  Examples Endless Examples & Exercises Given the values for capacitors in series or parallel circuits, calculate the total capacitance. Work these exercises until you are confident you have mastered the procedures. Note: The answers shown in these example often do not appear in normalized forms. For example, an answer appears as 1200F when it should be 1.2F.   Combination Capacitor Circuits Capacitors in SeriesParallel CombinationC_{T} = C_{1}  (C_{2} + C_{3})  Capacitors in ParallelSeries CombinationC_{T} = C_{1} + (C_{2}  C_{3}) 
