Question

The ratio of the resultant capacities when three capacitors of $2\mu F,4\mu F$ and $6\mu F$ are connected first in series and then in parallel is

• A. $1:11$
• B. $11:1$
• C. $12:1$
• D. $1:12$

Answer 1

The correct option is A $1:11$

When capacitor in series
$\frac{1}{C_{ef{f}_s}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

$\Rightarrow \frac{1}{C_{eff}}=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}$

$\Rightarrow \frac{1}{C_{eff}}=\frac{6+3+2}{12}$

$\Rightarrow C_{eff}=\frac{12}{11}$

$C_{{eff}_p}=C_1+C_2+C_3$

$=2+4+6$

$=12$

$\therefore \frac{C_S}{C_P}=\frac{1}{11}$