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MHT CET202416 May 2024Evening ShiftPhysicsCapacitanceActual

Air capacitor has capacitance ' C ₁ '. The space between two plates of capacitor is filled with two dielectrics as shown in figure. The new capacitance of the capacitor is ' C ₂ '. The ratio C ₁ C ₂ is ( d = distance between two plates of capacitor, K₁ and K₂ are dielectric constants of two dielectrics respectively)

Options

  1. AK ₁+ K ₂
  2. BK ₁+ K ₂ ~K ₁- K ₂
  3. C2 ~K ₁ ~K ₂ ~K ₁+ K ₂
  4. DK ₁+ K ₂ 2 ~K ₁ ~K ₂

Correct answer

D. K ₁+ K ₂ 2 ~K ₁ ~K ₂

Step-by-step solution

For an air capacitor, C ₁= A ₀ ~d When two dielectrics are inserted as shown, the combination acts as capacitors in series. aligned & 1 C ₂ = 1 CK ₁ + 1 CK ₂ & 1 C ₂ = 1 ~A ₀ ~K ₁ ~d 2 + 1 ~A ₀ ~K ₂ d 2 = d 2 ₀ ~A + ( 1 ~K ₁ + 1 ~K ₂ ) aligned aligned C₂ & = 2 ₀ A d + ( K₁ K₂ K₁+K₂ )= A ₀ d 2 A ₀ A d ( K₁ K₂ K₁+K₂ ) & = K₁+K₂ 2 K₁ K₂ aligned

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