Three identical capacitors C₁ , C₂ and C₃ , each of capacitance C , are connected to a DC source of voltage V . Capacitors C₁ and C₂ are connected in parallel, and their combination is connected in series with C₃ . What is the ratio of the energy stored in capacitor C₁ to the energy stored in capacitor C₃ ?

Step-by-step solution

The equivalent capacitance of the parallel combination of C₁ and C₂ is: C₁₂ = C + C = 2C This combination is connected in series with C₃ (capacitance C ) across the voltage source V . In a series circuit, the voltage divides inversely as the capacitance. The voltage across the parallel combination (which is the voltage across C₁ ) is: V₁ = V C₃ C₁₂ + C₃ = V C 2C + C = V 3 The voltage across C₃ is: V₃ = V C₁₂ C₁₂ + C₃ = V 2C 2C + C = 2V 3 The energy stored in capacitor C₁ is: U₁ = 1 2 C₁ V₁^2 = 1 2 C ( V 3 )^2 = CV^