Question

Five identical parallel conducting plates each of area A have separation 'd' between successive surface. The plates are connected to the terminal of a battery as shown in the figure. The effective capacitance of the circuit is

• A. $\frac{A{\epsilon }_0}{4d}$
• B. $\frac{4A{\epsilon }_0}{d}$
• C. $\frac{A{\epsilon }_0}{3d}$
• D. $\frac{3A{\epsilon }_0}{4d}$

Answer 1

The correct option is B $\frac{4A{\epsilon }_0}{d}$

Here five identical parallel plates will make four parallel plate capacitors and the capacitance of each capacitor is

$C=\frac{A{\epsilon }_0}{d}$

Here one plate of each capacitor is common for positive terminal and similarly other plate of each capacitor is common for negative terminal. Thus the four capacitors are in parallel configuration.

The effective capacitance , $C_{eff}=4C=\frac{4A{\epsilon }_0}{d}$