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)

$C_{1}=\frac{6 A \varepsilon_{0}}{2 d}=\frac{3 A \varepsilon_{0}}{d}$
$C_{2}=\frac{A \varepsilon_{0}}{2\left(d-\frac{d}{2}\left(1-\frac{1}{3}\right)-\frac{d}{2}\left(1-\frac{1}{6}\right)\right)}$
$C_{2}=\frac{A \varepsilon_{0}}{2\left(\frac{d}{6}+\frac{d}{12}\right)}$
$C_{2}=\frac{A \varepsilon_{0}}{2\left(\frac{d}{4}\right)}$
$C_{2}=\frac{2 A \varepsilon_{0}}{d}$
$C=C_{1}+C_{2}=\frac{5 A \varepsilon_{0}}{d}$