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)

$30\mu F$

Answer 2

$C_{R} = C_{1} + C_{2} = \frac{k_{1}\varepsilon_{0}A_{1}}{d} + \frac{k_{2}\varepsilon_{0}A_{2}}{d}$

$= \frac{2 \times \varepsilon_{0}\frac{A}{2}}{d} + \frac{4 \times \varepsilon_{0}\frac{A}{2}}{d} = 2 \times \frac{10}{2} + 4 \times \frac{10}{2} = 30\mu F$