CAIE A-Level Physics 19.1.3 Deriving Capacitor Combination Rules

Practise deriving equivalent capacitance for series and parallel combinations from C = Q/V, identifying shared charge or potential difference and checking units.

Exam points

derive the equivalent capacitance of capacitors in series from C = Q/V
derive the equivalent capacitance of capacitors in parallel from C = Q/V

[Maximum number: 2]

Three capacitors of capacitances $C_{1}, C_{2}$ and $C_{3}$ are initially uncharged. They are then connected in series to a battery, as shown in Fig. 7.1.

Fig. 7.1

The battery applies a potential difference V across the three capacitors.
Show that the combined capacitance C of the capacitors is given by

\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} .

$V=V_{1}+V_{2}+V_{3}$
either $\quad Q / C=Q / C_{1}+Q / C_{2}+Q / C_{3}$ or $V / Q=V_{1} / Q+V_{2} / Q+V_{3} / Q$
and so $1 / C=1 / C_{1}+1 / C_{2}+1 / C_{3}$

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19.1.3—C = Q / V, formulas for the combined capacitance of capacitors in series and question 1