A capacitor C₁ = 6 F is connected in series with a parallel combination of two capacitors C₂ = 1 F and C₃ = 2 F . A DC voltage V is applied across the entire system. What is the ratio of the charge on C₁ to the charge on C₂ ?

Step-by-step solution

First, find the equivalent capacitance of the parallel combination of C₂ and C₃ : C_p = C₂ + C₃ = 1 F + 2 F = 3 F The total equivalent capacitance of the circuit is: C_ eq = C₁ C_p C₁ + C_p = 6 3 6 + 3 = 2 F The total charge drawn from the source is: Q_ total = C_ eq V = 2V Since C₁ is in series with the rest of the circuit, the entire total charge flows through it: Q₁ = Q_ total = 2V This total charge Q_ total then splits between the parallel branches C₂ and C₃ in direct proportion to their capacitances. The charg