Question

The capacitance of an air filled parallel plate capacitor is $10\mu F$. The separation between the plates is doubled and the space between the plates is then filled with wax giving the capacitance a new value of $40\times 10^{-12}$ farads. The dielectric constant of wax is

• A. 12.0
• B. 10.0
• C. 8.0
• D. 4.2

Answer 1

Answer: (C)

$C_1=\frac{{\epsilon }_{0}A}{d}$
and $C_2=\frac{K{\epsilon }_{0}A}{2d}$
$\Rightarrow \frac{C_2}{C_1}=\frac{K}{2}$
$\Rightarrow \frac{40\times 10^{-12}}{10\times 10^{-12}}=\frac{K}{2}$
$\Rightarrow K=8$