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5.8: Kirchhoff’s Rules

  • Page ID
    6016
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    We can even adapt Kirchhoff’s rules to deal with capacitors. Thus, connect a 24 \(\text{V}\) battery across the circuit of Figure \(V.8\) – see Figure \(V.9\)

    V.9.png

    \(\text{FIGURE V.9}\)

    Calculate the charge held in each capacitor. We can proceed in a manner very similar to how we did it in Chapter 4, applying the capacitance equivalent of Kirchhoff’s second rule to three closed circuits, and then making up the five necessary equations by applying “Kirchhoff’s first rule” to two points. Thus:

    \[24-\frac{Q_2}{3}-\frac{Q_3}{2}=0,\label{5.8.1}\]

    \[24-Q_2-\frac{Q_4}{8},\label{5.8.2}\]

    \[\frac{Q_1}{3}-Q_2+\frac{Q_5}{4}=0,\]

    \[Q_1=Q_3+Q_5,\]

    \[Q_4=Q_2+Q_5,\]

    I make the solutions

    \[Q_1=+41.35\mu \text{C},\,Q_2=+19.01\mu \text{C},\,Q_3=+20.44\mu \text{C},\,Q_4 = +39.92 \mu \text{C},\,Q_5 =20.91 \mu \text{C}.\]


    This page titled 5.8: Kirchhoff’s Rules is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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