COMEDK202510 May 2025Evening ShiftPhysicsCapacitanceActual
By connecting two given capacitors, a technician was able to make two new capacitors having the effective capacitance 12.5 F and 2 F . What would be the capacitance of the given capacitors?
Options
- A8.5 ~F and 4 ~F
- B6.5 ~F and 6 ~F
- C10 ~F and 2.5 ~F
- D10.5 ~F and 2 ~F
Correct answer
C. 10 ~F and 2.5 ~F
Step-by-step solution
Let the capacitances of the two capacitors be C₁ and C₂ . When connected in parallel, the effective capacitance is C_p = C₁ + C₂ = 12.5 F . When connected in series, the effective capacitance is C_s = C₁ C₂ C₁ + C₂ = 2 F . Substituting C₁ + C₂ = 12.5 into the series formula: C₁ C₂ 12.5 = 2 C₁ C₂ = 25 . We have the sum S = C₁ + C₂ = 12.5 and the product P = C₁ C₂ = 25 . These are the roots of the quadratic equation x^2 - Sx + P = 0 . x^2 - 12.5x + 25 = 0 . Multiplying by 2 to clear decimals: 2x^2 - 25x + 50 = 0 . Us