Question

Consider a parallel plate capacitor of capacity $10\mu F$ with air filled in the gap between the plates. Now, one-half of the space between the plates is filled with a dielectric of dielectric constant $4$ as shown in the figure. The capacity of the capacitor changes to :

• A. $25\mu F$
• B. $20\mu F$
• C. $40\mu F$
• D. $5\mu F$

Answer 1

The correct option is A $25\mu F$

Given $\frac{{\epsilon }_{0}A}{d}=10$
Now both capacitors are in parallel
$C_1=\frac{{\epsilon }_{0}A/2}{d}$
$C_2=\frac{{K\epsilon }_0\left(A/2\right)}{d}$
$C^{{}^{\prime }}=\frac{{\epsilon }_{0}A/2}{d}+\frac{{4\epsilon }_0\left(A/2\right)}{d}=10[\frac{1}{2}+2]=25\mu F$