Question

There are four identical metal plates each of area $A$. The plates are placed at equal distance $d$ successively as shown in figure. If $\frac{A{ϵ}_0}{d}=2\mu F$ and source of emf $10V$ is connected between $x$ and $y$, then charge on plate $x$ will be

• A. $+30\mu C$
• B. $-30\mu C$
• C. $+20\mu C$
• D. $-20\mu C$

Answer 1

The correct option is A $+30\mu C$

The Potential of each plate will be,

The circuit can be rearranged as,
As the capacitor between plates $x$ and $A$ is equivalent to capacitor between $Y$ and $B$ , combination is connected to $10V$ battery in series. So, effective potential difference across each capacitor can be considered as $5V$

Charge on plate $x$ due to this loop is
$Q_{xA}=5\times 2=10\mu C$

As the capacitor between plates $x$ and $y$ is connected to $10V$ battery in series.
Charge on plate $x$ due to this loop is
$Q_{xy}=10\times 2=20\mu C$

Total charge
$Q=+30\mu C$