Question

When two capacitors are joined in series the resultant capacity is $2.4\mu F$ and when the same two are joined in parallel the resultant capacity is $10\mu F$. Their individual capacities are :

• A. $7\mu F,3\mu F$
• B. $1\mu F,9\mu F$
• C. $6\mu F,4\mu F$
• D. $8\mu F,2\mu F$

Answer 1

The correct option is C $6\mu F,4\mu F$

Let $C_1$ and $C_2$ be capacitors in series
$\frac{1}{C_{eff}}=\frac{1}{C_1}+\frac{1}{C_2}$
$\Rightarrow C_{eff}=\frac{1}{C_1}+\frac{1}{C_2}$
$\Rightarrow C_{eff}=\frac{C_1{C}_2}{C_1+C_2}=2.4$
In parallel
$C_{eff}=C_1+C_2=10$
$\Rightarrow C_1=10-C_2$
$\Rightarrow \frac{(10-C_2)\left(C_2\right)}{10}=2.4$
$\Rightarrow 10C_2-C_2^2=2.4$
$\Rightarrow C_2^2-10C_2+24=0$
$\Rightarrow C_2^2-6C_2-4C_2+24=0$
$\Rightarrow C_2(C_2-6C)-4(C_2-6)=0$
$\Rightarrow C_2=6or{C}_2=4$
$\therefore C_1=6and{C}_2=4$