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AC Components and Circuits
Capacitance
Section 5-5 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 | CT = | 1 | | 1 | + | 1 | + | 1 | | | | C1 | C2 | C3 | | | 
Capacitors in Parallel
CT = C1 + C2 + C3 | | Equations Total Capacitance of a Series Circuit | CT = | 1 | | 1 | + | 1 | + | 1 | + ... + | 1 | | C1 | C2 | C3 | Cn | Total Capacitance of a Parallel Circuit CT = C1 + C2 + C3 + ... + Cn Where - CT = Total capacitance of the series circuit
- C1, C2, C3, Cn = Values of all the individual capacitors
| | IMPORTANT The equations for total capacitance for series circuits uses the equation of a form for parallel-connected resistors and inductors. Likewise, the equation for parallel-connected capacitors has the same form as the equation for series-connected resistors and inductors. | The product-over-sum technique that is commonly used for pairs of parallel resistors works equally well for pairs of series capacitors. 
The shorthand notation for this equation is also to the parallel-resistance counterpart: CT = C1 || C2 | Example Problem Use the product-over-sum 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: 2. Substitute the given values | CT = | (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 CT = 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 Series-Parallel
CombinationCT = C1 || (C2 + C3) | 
Capacitors in Parallel-Series
CombinationCT = C1 + (C2 || C3) |
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