In the circuit shown, charge on the $5 mu mathrm{F}$ capacitor is :

Question:

In the circuit shown, charge on the $5 \mu \mathrm{F}$ capacitor is :

  1. (1) $18.00 \mu \mathrm{C}$

  2. (2) $10.90 \mu \mathrm{C}$

  3. (3) $16.36 \mu \mathrm{C}$

  4. (4) $5.45 \mu \mathrm{C}$


Correct Option: 1

Solution:

Let $q_{1}$ and $q_{2}$ be the charge on the capacitors of $2 \mu \mathrm{F}$ and $4 \mu \mathrm{F}$. Then charge on capacitor of $5 \mu \mathrm{F}$

$Q=q_{1}+q_{2}$

$\Rightarrow 5 V_{0}=2\left(6-V_{0}\right)+4\left(6-V_{0}\right)$

$\Rightarrow 5 V_{0}=12-2 V_{0}+24-4 V_{0}$

$\Rightarrow 11 V_{0}=36 \Rightarrow V_{0}=\frac{36}{11} V$

$\Rightarrow Q=5 V_{0}=\frac{180}{11} \mu C$

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