Question

The charge on the $4\mu \text{F}$ capacitor in the given circuit is ____ (in $\mu \text{C})$.

• A. $12$
• B. $24$
• C. $36$
• D. $32$

Answer 1

The correct option is B $24$

Equivalent capacitance of top right branch in which $1\mu \text{F}$ and $5\mu \text{F}$ are in parallel will be

$C_{eq}^{\prime }=5+1=6\mu \text{F}$


Since, $4\mu \text{F}$ and $6\mu \text{F}$ are in series, so effective capacitance of these two capacitors will be

$C_{eq}=\frac{4\mu \text{F}\times 6\mu \text{F}}{4\mu \text{F}+6\mu \text{F}}=2.4\mu \text{F}$

And voltage across the $2.4\mu \text{F}$ capacitor will be $10\text{V}$. So charge $Q$ on $2.4\mu \text{F}$ will be

$Q=C_{eq}V=2.4\mu \text{F}\times 10\text{V}=24\mu \text{C}$

Here, whatever charge this equivalent capacitance will have, the same charge will be across the $4\mu \text{F}$ capacitor as well as the equivalent of $1\mu \text{F}$ and $5\mu \text{F}$ which is $6\mu \text{F}$.

So, Charge on $4\mu \text{F}$ capacitor is $Q=24\mu \text{C}$.

Hence, option $\left(b\right)$ is correct.