Question

Find charge on each capacitor in the given circuit?

• A. $46\mu \text{C},54\mu \text{C},7\mu \text{C}$
• B. $66\mu \text{C},7.5\mu \text{C},58.5\mu \text{C}$
• C. $58.5\mu \text{C},7.5\mu \text{C},60\mu \text{C}$
• D. $7.5\mu \text{C},36\mu \text{C},55\mu \text{C}$

Answer 1

The correct option is B $66\mu \text{C},7.5\mu \text{C},58.5\mu \text{C}$

Using potential method, we can solve this problem, assigning potential to known points, as shown in figure.

Using Kirchhoff`s junction law, net charge on the isolated part of circuit must be zero.

$(V_0-12)8+(V_0-0)2+(V_0-(-6\left)\right)6=0$

$\Rightarrow 8V_0-96+2V_0+6V_0+36=0$

$\Rightarrow 16V_0=60$

$\therefore V_0=\frac{15}{4}\text{V}$

Using $V_0$, we can get charge on each capacitor.

Charge on $C_1$:

$\Rightarrow Q_1=C_1{V}_{PDacross{C}_1}=8(12-\frac{15}{4})=66\mu \text{C}$

Similarly, $Q_2$ and $Q_3$ as follows,

$Q_2=C_2{V}_{PDacross{C}_2}=2(\frac{15}{4}-0)=7.5\mu \text{C}$

$Q_3=C_3{V}_{PDacross{C}_3}=6(\frac{15}{4}-(-6\left)\right)=58.5\mu \text{C}$

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