Physics - Capacitor Question with Solution | TestHub

The capacitors $2C$, $3C$, and $4C$ are connected in parallel. Their equivalent capacitance is:
$C_p=2C+3C+4C=9C$

This combination is in series with $C^1$. The total equivalent capacitance between A and B is $6C$.

Using the formula for series combination:
$\frac{1}{C_{eq}}=\frac{1}{C_p}+\frac{1}{C^1}$

$\frac{1}{6C}=\frac{1}{9C}+\frac{1}{C^1}$

$\frac{1}{C^1}=\frac{1}{6C}-\frac{1}{9C}$

$\frac{1}{C^1}=\frac{3-2}{18C}=\frac{1}{18C}$

$C^1=18C$

Answer: $18C$