Question

A parallel plate capacitor with air between the plates has a capacitance of $10\mu F$. The area of the capacitor is divided into two equal halves and filled with two media having dielectric constants $K_1=2$ and $K_2=4$. The capacitance of the system will be:

• A. $10\mu F$
• B. $20\mu F$
• C. $30\mu F$
• D. $40\mu F$

Answer 1

The correct option is C $30\mu F$

Capacitor filled with air,
$10\mu F=A{ϵ}_0/d$
$C_1=(A/2\times {ϵ}_0\times {\kappa }_1)/d=A{ϵ}_0/d=10\mu F$
$C_2=(A/2\times {ϵ}_0\times {\kappa }_2)/d=2A{ϵ}_0/d=20\mu F$
As they are connected in parallel,
$C_{net}=C_1+C_2=30\mu F$