Question

If the surface area of each surface of a plate is $A$ and separation between two adjacent plates is $d$. Calculate the charge given by the battery.

• A. $\frac{2}{3}\left(\frac{{\epsilon }_{0}A}{d}\right)V_0$
• B. $\frac{3{\epsilon }_{0}A}{d}{V}_0$
• C. $\frac{{\epsilon }_{0}A}{d}{V}_0$
• D. $\frac{1}{4}\frac{{\epsilon }_{0}A}{d}{V}_0$

Answer 1

The correct option is A $\frac{2}{3}\left(\frac{{\epsilon }_{0}A}{d}\right)V_0$

The given circuit is,


Its equivalent circuit can be;

Here,

$C_{eq}=\frac{2C}{3}$

as we know, that charge given by the battery is,

$Q=C_{eq}V$

$\therefore Q=\frac{2}{3}C{V}_0$

As we know that capacitance for parallel plate capacitor is given by,

$C=\frac{{\epsilon }_{0}A}{d}$

Therefore, the net charge provided by the battery is,
$Q=\frac{2}{3}\left(\frac{{\epsilon }_{0}A}{d}\right)V_0$