Capacitors in Circuits: Series and Parallel

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Section 27.1 Capacitors in Circuits: Series and Parallel

You learned about capacitors in Section Capacitors. Capacitors can also be elements within a circuit!

Video Lesson 27.1.1. Capacitors in Series and Parallel.

Subsubsection Key Ideas

Combining capacitors in series and in parallel is opposite to how you combine resistors.

Two parallel lines of equal length representing a capacitor. — Figure 27.1.2. The circuit diagram representation for a capacitor.
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Subsubsection Activities

Activity 27.1.1. Capacitor Arrangements.

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.
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Capacitors in series have the same charge.
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Capacitors in parallel have the same voltage.
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Capacitors in parallel have the same charge.
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Explain your reasoning.

In class, you will derive the rules below for combining capacitors.

Definition 27.1.3. 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 27.1.4. 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*}