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JEE MainPhysicsCapacitance

Three capacitors of capacitances 12 F , 6 F , and an unknown capacitance C are connected in series across a 20 V battery. If the charge on the 6 F capacitor is 48 C , the value of the unknown capacitance C is

Options

  1. A4 F
  2. B6 F
  3. C12 F
  4. D2.4 F

Correct answer

B. 6 F

Step-by-step solution

In a series circuit, the charge on all capacitors is equal. Therefore, the charge on each capacitor is Q = 48 C . The voltage across the 12 F capacitor is V₁ = Q C₁ = 48 12 = 4 V . The voltage across the 6 F capacitor is V₂ = Q C₂ = 48 6 = 8 V . The total voltage is the sum of the voltages across each capacitor: V_ total = V₁ + V₂ + V_C 20 = 4 + 8 + V_C V_C = 8 V The capacitance of the unknown capacitor is C = Q V_C = 48 8 = 6 F . Answer: 6 F

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