Question

Three different dielectrics are filled in a parallel plate capacitor as shown. What should be the dielectric constant of a material, which when fully filled between the plates produces same capacitance?

• A. 4
• B. 6
• C. 5
• D. 9

Answer 1

Answer: (C)

$C_1=\frac{6A{\epsilon }_0}{2d}=\frac{3A{\epsilon }_0}{d}$
$C_2=\frac{A{\epsilon }_0}{2\left(d-\frac{d}{2}\left(1-\frac{1}{3}\right)-\frac{d}{2}\left(1-\frac{1}{6}\right)\right)}$
$C_2=\frac{A{\epsilon }_0}{2\left(\frac{d}{6}+\frac{d}{12}\right)}$
$C_2=\frac{A{\epsilon }_0}{2\left(\frac{d}{4}\right)}$
$C_2=\frac{2A{\epsilon }_0}{d}$
$C=C_1+C_2=\frac{5A{\epsilon }_0}{d}$