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AP EAMCET20227 Jul 2022Morning ShiftPhysicsCapacitanceActual

A capacitor has capacitance C₀ when there is no dielectric between it's plates. 2 slabs of dielectric constant K₁, K₂ respectively with area equal to area of plates but thickness half of the distance between the plates are placed in between the plates. Then the new capacitance is

Options

  1. AC₀ (K₁+K₂ )
  2. BC₀ ( K₁ K₂ K₁+K₂ )
  3. CC₀ ( K₁+K₂ K₁ K₂ )
  4. D2 C₀ ( K₁ K₂ K₁+K₂ )

Correct answer

D. 2 C₀ ( K₁ K₂ K₁+K₂ )

Step-by-step solution

Initial capacitance of capacitor, C₀= ₀ A d Now, capacitor is filled with two dielectrics each slab has area A and distance d / 2 as shown Above arrangement is a series combination of two capacitors as shown so, capacity of above arrangement is 1 C_ eq = 1 C₁ + 1 C₂ aligned & = 1 ₀ K₁ A (d / 2) + 1 ₀ K₂ A /(d / 2) & = d 2 ₀ A [ 1 K₁ + 1 K₂ ] aligned aligned & 1 C_ eq = d 2 ₀ A [ K₁+K₂ K₁ K₂ ] & C_ eq = 2 ₀ A d [ K₁ K₂ K₁+K₂ ] & C_ eq =2 C₀ ( K₁ K₂ K₁+K₂ ) aligned

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