Question

A parallel plate capacitor of area A and plate separation d is filled with two dielectrics as shown. What is the capacitance of the arrangement?

• A. \(\dfrac{3K\varepsilon_0A}{4d}\)
• B. \(\dfrac{4K\varepsilon_0A}{3d}\)
• C. \(\dfrac{(K+1)\varepsilon_0A}{2d}\)
• D. (K(K+3)varepsilon₀A)/(2(K+1)d)

Hint:

Divide complex dielectric systems into simple series or parallel capacitors.

Answer 1

The Correct Option is A

Step 1: The capacitor behaves as two capacitors in parallel.
Step 2: Capacitances: C₁ = (Kvarepsilon₀(A/2))/(d/2), C₂ = (Kvarepsilon₀(A/2))/(d)
Step 3: Total capacitance: C = C₁ + C₂ = (3Kvarepsilon₀A)/(4d)