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The effective capacitance of two capacitors of capacitances C 1 and C 2 C 2 > C 1 connected in parallel is 25 6 times the effective capacitance when they are connected in series. The ratio C 2 C 1 is

Options

  1. A3 2
  2. B4 3
  3. C5 3
  4. D25 6

Correct answer

A. 3 2

Step-by-step solution

C p a r a l l e l = 25 6 C s e r i e s ⇒ C 1 + C 2 = 25 6 C 1 C 2 C 1 + C 2 ⇒ 6 C 1 + C 2 2 = 25 C 1 C 2 ⇒ 6 C 1 2 + 6 C 2 2 + 12 C 1 C 2 = 25 C 1 C 2 ⇒ 6 C 1 2 C 2 2 + 6 + 12 C 1 C 2 = 25 C 1 C 2 ⇒ 6 C 1 2 C 2 2 - 13 C 1 C 2 + 6 = 0 This is quadratic equation By solving we get C 2 C 1 = 3 2

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