Aparallel-plate capacitor is connected to a cell. Its positive pl… - Vidyadip

MCQ

Aparallel-plate capacitor is connected to a cell. Its positive plate $A$ and its negative plate $B $ have charges $+Q$ and $-Q$ respectively. A third plate $C$, identical to $A$ and $B$, with charge $+Q$, is now introduced midway between $ A$ and $B$, parallel to them. Which of the following are correct?

A
The charge on the inner face of $B$ is now $ - \frac{{3Q}}{2}$
B
There is no change in the potential difference between $A$ and $B$.
C
The potential difference between $A$ and $C$ is one-third of the potential difference between $B$ and $C$.
✓
all of the above

✓

Answer

Correct option: D.

all of the above

d
Now the charge on outer surfaces should be same

$q=Q-q \Rightarrow q=Q / 2$

So $(A)=-2 Q+Q / 2=-3 Q / 2$

Charge on $\mathrm{A}=\mathrm{Q} / 2$ and charge on $\mathrm{B}=3 \mathrm{Q} / 2$

So as $E \propto Q$ and $V \propto E \Rightarrow V \propto Q$

and hence $C$ is correct.

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