Question

Three capacitors of capacitances 3 $\mu$ F, 9 $\mu$ F and 18 $\mu$ F are connected once in series and another time in parallel. The ratio of equivalent capacitances in the two cases will be

• A. 1:15
• B. 12:11
• C. 1:1
• D. 1:3

Answer 1

The correct option is A 1:15

$C_1=3\mu F,C_2=9\mu F,C_3=18\mu F$
When connected in serries,
$\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$
$\frac{1}{C_s}=\frac{1}{3}+\frac{1}{9}+\frac{1}{18}=\frac{6+2+1}{18}=\frac{9}{18}=\frac{1}{2}$
$C_s=2\mu F$
When connected in parallel,
$C_p=C_1+C_2+C_3=3+9+18=30\mu F$
Ratio of equivalent resistance in series to parallel combination = 2:30 = 1:15