Capacitors $C_1=4\mu \text{F}$ and $C_2=6\mu \text{F}$ are connected in series. This series combination is then connected in parallel with a capacitor $C_3=5\mu \text{F}$. Find the equivalent capacitance of the whole network.

Step-by-step solution

1. First find the equivalent capacitance of the series pair:
2. For series, $\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}=\frac{1}{4}+\frac{1}{6}=\frac{3+2}{12}=\frac{5}{12}$.
3. Invert to get $C_s=\frac{12}{5}=2.4\mu \text{F}$.
4. Now add the parallel capacitor $C_3$:
5. For parallel, $C_{\text{eq}}=C_s+C_3=2.4\mu \text{F}+5\mu \text{F}=7.4\mu \text{F}$.

Concept tested: Series‑parallel combination of capacitors

Published 10 September 2026 · How this solution was prepared and checked