Two dielectric of dielectric constants ϵ1 & ϵ2 are inserted between the plates

Question

Two dielectric of dielectric constants \(\epsilon _1 \ \&\ \epsilon_2\) are inserted between the plates of two identical parallel plate capacitors as shown in the figure. The ratio of their capacitances \(C_2/C_1\) is \((\text{Given} \frac{\epsilon _1}{\epsilon _2} = 2):-\) 

(1) \(\frac{9}{8}\)

(2) \(\frac{7}{8}\)

(3) \(\frac{8}{7}\)

(4) \(\frac{8}{9}\)

Answer 1

Correct option is : (1) \(\frac{9}{8}\)

\(C_1^{**} = \frac{2k \frac{A}{2}\varepsilon_0}{d} = C_0 \ (\text{Let})\)

\(C_2^{**} = \frac{2\frac{A}{2}\varepsilon _0}{d} = \frac{C_0}{2}\)

\(C_2 = \frac{3 C_0}{2}\)