Question

The capacitors of three capacities are in the ratio 1 : 2 : 3. Their equivalent capacity when connected in parallel is $\frac{60}{11}\mu F$ more than that when connected in series. The individual capacities are :

• A. 4, 6, 7
• B. 1, 2, 3
• C. 2, 3, 4
• D. 1, 3, 6

Answer 1

Answer: (B)

1, 2, 3

Let the capacitance be,
C, 2C and 3C .
in series
$\frac{1}{C_{eff}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$
$\Rightarrow \frac{1}{C_{eff}}=\frac{1}{C}+\frac{1}{2C}+\frac{1}{3C}$
$\Rightarrow \frac{1}{C_{eff}}=\frac{6+3+2}{6C}$
$\Rightarrow c_{eff}=\frac{6C}{11}$
in parallel
$C_{eff}=C_1+C_2+C_3$
$\Rightarrow C_{eff}=C+2C+3C$
$=6C$
given parallel connection $=\frac{60}{11}\mu F$ more than the series connection
$\Rightarrow 6C=\frac{60}{11}\mu F+\frac{6C}{11}$
$\Rightarrow \frac{60C}{11}=\frac{60}{11}\mu F$
$\Rightarrow C=1\mu F;2C=2\mu F;3C=3\mu F$