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COMEDK2023Evening ShiftPhysicsCapacitanceActual

In the figure, first the capacitors are fully charged by closing the key K . Then after opening the Key a dielectric material with dielectric constant 2 is filled in the space between the plates of both the capacitor. At this state the ratio of the Charge on the capacitor C₁ to that of C₂ is:

Options

  1. A2 : 1
  2. B1 : 1
  3. C1 : 2
  4. D3 : 2

Correct answer

A. 2 : 1

Step-by-step solution

When key K is closed, both C₁ and C₂ ( = 1 F each) are connected to the 12V battery. Initial charge on both: Q₁ = Q₂ = 1 F 12 V = 12 C When key K is opened, C₂ gets isolated — its charge stays constant at 12 C . C₁ remains connected to the battery. Dielectric with k = 2 is inserted in both. New capacitances: C₁' = C₂' = 2 F For C₁ (still connected to battery, V = 12 V ): Q₁' = 2 F 12 V = 24 C For C₂ (isolated, charge conserved): Q₂' = 12 C Q₁' Q₂' = 24 12 = 2 1

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