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Section 26.11 Capacitors in Circuits
Activity 26.11.1. Warmup: Capacitor Arrangements.
Which of the following statements about capacitors do you think is true? (You may select more than one answer.)
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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.
Video Lesson 26.11.1. Capacitors in Series and Parallel.
Assumption 26.11.2. Capacitor Voltage.
The definition of
Capacitance \(C\) can be rewritten to establish the voltage across a capacitor with charge
\(Q\) on its positive plate.
\begin{equation*}
V = \frac{Q}{C}
\end{equation*}
The voltage in a capacitor is higher on the side with positive charge.
Combining capacitors in series and in parallel is opposite to how you combine resistors.
Definition 26.11.4. 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 26.11.5. 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*}
