# Series capacitor equivalence

I have capacitors of 100uF, 10uF and 1uF; and need a series circuit with these capacitors to form a 0.1uF capacitor, is this possible?

# Capacitors associations

## Series association

This association gives a lower total capacity than any of its component capacitors. The total capacity, for $n$ capacitors is

$$C_{eq} = \dfrac{1}{\sum\limits_{n}\dfrac{1}{C_n}}$$

## Parallel association

This association gives a greater total capacity than any of its component capacitors. The total capacity, for $n$ capacitors is

$$C_{eq} = \sum\limits_nC_n$$

So, for your question, the answer is yes. You must connect 10 capacitors of 1$\mu$F in series.

The equivalent capacitance $C_{eq}$ of $n$ capacitors $C_{1}$, $C_{2}$, $\ldots C_{n}$ in series is

$$\frac{1}{C_{eq}} = \sum_{i = 1}^{n}\frac{1}{C_{i}}$$

In your case you can connect 10 $1\mu$F capacitors in series for an equivalent capacitance of $0.1\mu$F.