Question

A parallel plate capacitor with air as medium between the plates has a capacitance of $10\mu F$. The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant $k_1=2$ and $k_2=4$. The capacitance of the system will now be

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

Answer 1

Answer: (C)

$C_R=C_1+C_2=\frac{k_1{\epsilon }_0{A}_1}{d}+\frac{k_2{\epsilon }_0{A}_2}{d}$
$=\frac{2\times {\epsilon }_0\frac{A}{2}}{d}+\frac{4\times {\epsilon }_0\frac{A}{2}}{d}$
$=2\times \frac{10}{2}+4\times \frac{10}{2}=30\mu F$