Two unknown capacitors are connected across a 10 ~V DC supply. When they are connected in parallel, the total charge drawn from the supply is 250 C . When they are connected in series across the same supply, the total charge drawn is 40 C .

Question

Two unknown capacitors are connected across a 10 ~V DC supply. When they are connected in parallel, the total charge drawn from the supply is 250 C . When they are connected in series across the same supply, the total charge drawn is 40 C . The individual capacitances of the two capacitors are:

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Correct answer: C. 20 F , 5 F

Let the capacitances be C₁ and C₂ . When connected in parallel, the equivalent capacitance is C_p = C₁ + C₂ . The total charge drawn is Q_p = C_p V . (C₁ + C₂) 10 = 250 C₁ + C₂ = 25 F When connected in series, the equivalent capacitance is C_s = C₁ C₂ C₁ + C₂ . The total charge drawn is Q_s = C_s V . C₁ C₂ C₁ + C₂ 10 = 40 C₁ C₂ 25 10 = 40 C₁ C₂ = 100 ( F )^2 Solving the equations C₁ + C₂ = 25 and C₁ C₂ = 100 , we get a quadratic equation: C^2 - 25C + 100 = 0 (C - 20)(C - 5) = 0 Thus, the individual capacitances are

Two unknown capacitors are connected across a 10 ~V DC supply. When they are connected in parallel, the total charge drawn from the supply is 250 C . When they are connected in series across the same supply, the total charge drawn is 40 C . The individual capacitances of the two capacitors are:

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