Question

A capacitor is half filled with a dielectric $(K=2)$ as shown in figure $A$. If the same capacitor is to be filled with same dielectric as shown, what would be the thickness of dielectric so that capacitor still has same capacity?

• A. 2d/3
• B. 3d/2
• C. 3d/4
• D. 4d/3

Answer 1

Answer: (A)

$C_{\text{net }}=\frac{k+1}{2}\frac{A{\epsilon }_0}{d}$
$C_{\text{net }}=\frac{A{\epsilon }_0}{d-t\left(1-\frac{1}{2}\right)}=\frac{A{\epsilon }_0}{d-\frac{t}{2}}$
$C_{\text{net }}=\frac{3A{\epsilon }_0}{2d}$
$\frac{3A{\epsilon }_0}{2d}=\frac{A{\epsilon }_0}{d-\frac{t}{2}}$
$3d-\frac{3t}{2}=2d$
$\frac{3t}{2}=d$
$t=\frac{2d}{3}$