Question

Three capacitors $3\mu F,9F$ and $18\mu F$ are connected first in series and then in parallel. The ratio of the equivalent capacitance in two cases is :

• A. $15:1$
• B. $1:1$
• C. $1:15$
• D. $1:3$

Answer 1

The correct option is A $15:1$

Given, Three capacitors $3\mu f,9\mu f,18\mu f$

So, the capacitor connected in the series,

$\frac{1}{C_{eq}}=\frac{1}{c_1}+\frac{1}{C_2}\frac{1}{C_3}\Rightarrow =\frac{1}{3}+\frac{1}{9}+\frac{1}{18}$

$=\frac{6+2+1}{18}=\frac{9}{18}=\frac{1}{2}\Rightarrow C_{eq}=2$

And the capacitor is connected in parallel $C_{eq}=3+9+18=30$

So, the ratio of the series and the parallel is:

$\frac{C_{eq}}{C_{eq}}=\frac{30}{2}=15:1$