## University Physics with Modern Physics (14th Edition)

$C_{new} = 57 \mathrm{~\mu F}$
Capacitors $12 \mathrm{~\mu F}$ and $6 \mathrm{~\mu F}$ are in series, therefore their equivalent capacitor is given by $$\dfrac{1}{{C}'} = \dfrac{1}{12\mathrm{~\mu F} } + \dfrac{1}{6 \mathrm{~\mu F} } = 0.25$$ Take the reciprocal $${C}' = 4 \mathrm{~\mu F}$$ ${C}'$, $11 \mathrm{~\mu F}$ and the new capacitor $C_{new}$ are in parallel where their equivalent capacitance is calculated by $${C}'' = 11 \mathrm{~\mu F} + C_{new} + {C}' = 15 \mathrm{~\mu F} +C_{new}$$ This combination ${C}''$ is in series with $9 \mathrm{~\mu F}$ and their equivalent in series is ${C}''' = 8 \mathrm{~\mu F}$ and we could get $C_{new}$ in the next \begin{gather*} \dfrac{1}{{C}''' } = \dfrac{1}{9 \mathrm{~\mu F} } + \dfrac{1}{15 \mathrm{~\mu F} +C_{new}}\\ \dfrac{1}{15 \mathrm{~\mu F} +C_{new}} = \dfrac{1}{{C}''' } - \dfrac{1}{9 \mathrm{~\mu F} } \\ \dfrac{1}{15 \mathrm{~\mu F} +C_{new}} = \dfrac{1}{72 \mathrm{~\mu F} }\\ 15 \mathrm{~\mu F} +C_{new} = 72 \mathrm{~\mu F} \\ \boxed{C_{new} = 57 \mathrm{~\mu F} } \end{gather*}