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MHT CET202522 Apr 2025Morning ShiftPhysicsCapacitanceActual

A series combination of 10 capacitors, each of value ' C ₁ ' is charged by a source of potential difference ' 4 V '. When another parallel combination of 8 capacitors, each of value ' C ₂ ' is charged by a source of potential difference ' V ', it has the same total energy stored in it as in the first combination. The value of ' C ₂ ' is

Options

  1. AC ₁ 5
  2. B8 5 C₁
  3. C64 5 C₁
  4. DC ₁ 40

Correct answer

A. C ₁ 5

Step-by-step solution

The equivalent capacitance of 10 identical capacitors C₁ in series is C_ eq1 = C₁ 10 . When charged to 4V , the stored energy becomes U₁ = 1 2 C₁ 10 (4V)^2 = 4 5 C₁ V^2 . For 8 capacitors C₂ in parallel, the equivalent capacitance is C_ eq2 = 8C₂ . The stored energy at voltage V is U₂ = 1 2 8C₂ V^2 = 4C₂ V^2 . Equating the energies yields 4 5 C₁ V^2 = 4C₂ V^2 , which simplifies to C₂ = C₁ 5 . This corresponds to option A .

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