Question

The capacity of a parallel plate condenser with air medium is 60$\mu F$ having distance of separation d . If the space between the plates is filled with two slabs each of thickness d/2 and dielectric constants 4 and 8, the effective capacity becomes :

• A. 160$\mu$ F
• B. 320$\mu$ F
• C. 640$\mu$ F
• D. 360$\mu$ F

Answer 1

The correct option is B 320$\mu$ F

Given initial capacitance
$C=60\mu F$
$\Rightarrow 60\mu F=\frac{{\epsilon }_{0}A}{d}$
When the distance is filled with materials with different dielectric medium we have two capacitance
$C_1=\frac{k_1{\epsilon }_{0}A}{\left(\frac{d}{2}\right)}$ and $C_2=\frac{k_2{\epsilon }_{0}A}{\left(\frac{d}{2}\right)}$ in series.
$C_1=4\times 60\times 2\mu F{C}_2=8\times 60\times 2\mu F$
$C_1=480\mu F$ and $C_2=960\mu F$
We know, when capacitors are in series:
$\frac{1}{c_{eff}}=\frac{1}{c_1}+\frac{1}{c_2}$
$\therefore \frac{1}{c_{eff}}=\frac{1}{480}+\frac{1}{960}\Rightarrow C_{eff}=320\mu F.$