Question

Two identical parallel plate (air) capacitors C₁ and C₂ have capacitances C each. The space between their plates is now filled with dielectrics as shown. If the two capacitors still have equal capacitance, obtain the relation between dielectric constants K, K₁ and K₂.

Answer 1

Let A → area of each plate.

Let initially C₁ = C = \(\cfrac{\varepsilon_0A}d \) = C₂....(i)

After inserting respective dielectric slabs:

and C'₂ = K₁\(\cfrac{\varepsilon_0(A/2)}d+\cfrac{K_2\varepsilon_0(A/2)}d\)....(ii)

From (i) and (ii)

C'₁ = C'₂

⇒ KC = \(\cfrac{C}2\)(K₁ + K₂)

⇒ K = \(\cfrac{1}2\)(K₁ + K₂)