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MHT CET202416 May 2024Morning ShiftPhysicsCapacitanceActual

A series combination of n₁ capacitors, each of value C₁ is charged by a source of potential difference 6 V . Another parallel combination of n ₂ capacitors, each of value C ₂ is charged by a source of potential' difference 2 V . Total energy of both the combinations is same. The value of C ₂ in terms of C ₁ is

Options

  1. A3 C₁ n₁ n₂
  2. B9 n ₂ n ₁ C ₁
  3. C3 n ₂ n ₁ C ₁
  4. D9 C₁ n₁ n₂

Correct answer

D. 9 C₁ n₁ n₂

Step-by-step solution

When connected in series, ( C _ eq )₁= C ₁ n ₁ ; V ₁=6 ~V When connected in parallel, ( C _ eq )₂= n ₂ C ₂ ; V ₂=2 ~V Total energy is the same for both connections, U ₁= U ₂ aligned & 1 2 ( C _ eq )₁ ~V ₁^2= 1 2 ( C _ eq )₂ ~V ₂^2 ( U = 1 2 CV ^2 ) & 1 2 C ₁ n ₁ 36= 1 2 n ₂ C ₂ 4 & C ₂= 9 C ₁ n ₁ n ₂ aligned

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