Section 10.12 Capacitors in Circuits: Series and Parallel
You learned about capacitors in Section
Section 9.21. Capacitors can also be elements within a circuit!
Combining capacitors in series and in parallel is opposite to how you combine resistors.
Figure 10.12.1. The circuit diagram representation for a capacitor.
Exercises Activities
1.
Which of the following statements about capacitors do you think is true? (You may select more than one answer.)
Capacitors in series have the same voltage.
Capacitors in series have the same charge.
Capacitors in parallel have the same voltage.
Capacitors in parallel have the same charge.
Explain your reasoning.
In class, you will derive the rules below for combining capacitors.
Definition 10.12.2. Combining Capacitors in Series.
If \(N\) capacitors are in series, the equivalent capacitance is:
\begin{equation*}
\frac{1}{C_{\mathrm{eq}}} = \sum_{i = 1}^{N} \frac{1}{C_i} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots
\end{equation*}
Definition 10.12.3. Combining Capacitors in Parallel.
If \(N\) capacitors are in parallel, the equivalent capacitance is:
\begin{equation*}
C_{\mathrm{eq}} = \sum_{i = 1}^{N} C_i = C_1 + C_2 + C_3 + \dots
\end{equation*}
