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.

 CT = C1C2 C1 + C2

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:

 CT = C1C2 C1 + C2

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)