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MHT CET202124 Sep 2021Evening ShiftPhysicsCapacitanceActual

Capacitors of capacities C ₁, C ₂ and C ₃ are connected in series. If the combination is connected to a supply of ' V ' volt, then potential difference across capacitor ' C ₁ ' is

Options

  1. AC ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂ C ₁ C ₂ ~V
  2. BC ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂ C ₁ C ₂ C ₃ ~V
  3. CC ₂ C ₃ ~V C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂
  4. DC ₁ C ₂ C ₃ ~V C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂

Correct answer

C. C ₂ C ₃ ~V C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂

Step-by-step solution

In series combination, the equivalent capacitance C is given by aligned & 1 C = 1 C ₁ + 1 C ₂ + 1 C ₃ & 1 C = C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂ C ₁ C ₂ C ₃ aligned C = C ₁ C ₂ C ₃ C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂ Charge Q stored by the combination is given by Q = CV = C ₁ C ₂ C ₃ ~V C ₂ C ₃+ C ₁ C ₃+ C ₁ C ₂ Charge on each capacitor is same. Hence potential difference Charge on each capacitor is same. Hence potential difference across C₁ is V₁= Q C₁ = C₂ C₃ V C₂ C₃+C₁ C₃+C₁ C₂

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