Question

Two capacitors $C_1$ and $C_2$ are charged to $120\text{V}$ and $200\text{V}$ respectively. It is found that by connecting them together, the potential difference on each one can be made zero. Then:

• A. $5C_1=3C_2$
• B. $3C_1=5C_2$
• C. $3C_1+5C_2=0$
• D. $9C_1=4C_2$

Answer 1

The correct option is B $3C_1=5C_2$

After charging the capacitors to the respective potential difference, charges will appear on their positive and negative plates.



Thus, $q_1=120C_1$ and $q_2=200C_2$

The condition for obtaining zero potential difference after connecting them together, it is only possible when charge on capacitor becomes zero $(q=0)$.

This is only possible when $+ve$ plate of one of the capacitor is connected to $-ve$ plate of the other.


$\therefore q_1-q_2=0$

(Net charge on combination of plates as shown in figure)

$\Rightarrow 120C_1-200C_2=0\Rightarrow 3C_1-5C_2=0$

$\therefore 3C_1=5C_2$

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

Why this question ? When the capacitor plates of opposite polarity are connected, the net charge will be as per law of charge conservation because for air plate capacitors it gives rise to an isolated system for "connected plates".