Question

A parallel plate capacitor with air as the medium 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 constant $k_1=2$ and $k_2=4$. The capacitance will now 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

Initial capacitance is given as $C=10\mu F$
$\Rightarrow C=\frac{{\epsilon }_{0}A}{d}=10\mu F$
New arrangement acts as two capacitors $C_1$ and $C_2$ connected in parallel.
Thus capacitance of each part $C_1=\frac{k_1{\epsilon }_0{A}_1}{d}$ and $C_2=\frac{k_2{\epsilon }_0{A}_2}{d}$
Equivalent capacitance of parallel combination $C_p=C_1+C_2=(k_1+k_2)\frac{{ϵ}_0(A_1+A_2)}{d}$

$⟹$ $C_p=(k_1+k_2)\frac{{ϵ}_{0}A}{2d}$ $(\because A_1=A_2=\frac{A}{2})$
Thus $C_p=(2+4)\times \frac{10}{2}=30\mu F$