Question

Find the charge through capacitor $C_3$ in the given circuit?

• A. $70\mu \text{C}$
• B. $30\mu \text{C}$
• C. $90\mu \text{C}$
• D. $10\mu \text{C}$

Answer 1

The correct option is C $90\mu \text{C}$

Let the potential at $\text{M}$ be $V_1$ and potential at $\text{N}$ be $V_2$.

As we know that, amount of charge leaving through a point is equal to the amount of charge coming through it.



we can say from the diagram that,

At $\text{M}:$

$10\times (V_1-14)+10\times (V_1-V_2)+5\times (V_1-0)=0$

$\Rightarrow 10V_1-140+10V_1-10V_2+5V_1=0$

$\Rightarrow 25V_1-10V_2=140....\left(1\right)$

At $\text{N}:$

$5\times (V_2-14)+10\times (V_2-V_1)+10\times (V_2-0)=0$

$\Rightarrow 5V_2-70+10V_2-10V_1+10V_2=0$

$\Rightarrow 25V_2-10V_1=70....\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get,

$V_1=8\text{V},V_2=-1\text{V}$

Thus, Charge passing through $C_3$ is given by $Q_3=C_3|V_1-V_2|=10\times (8-(-1)=90\mu \text{C}$

Hence, option (c) is the correct answer.