Series capacitor equivalence

Question

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?

Answer 1

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.

Answer 2

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.