Consider the combination of two capacitors C 1 and C 2 , with C 2 > C 1 , when connected in parallel, the equivalent capacitance is 10 times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, C 2 C 1 .

Step-by-step solution

When connected in parallel C e q = C 1 + C 2 When in series C eq ' = C 1 C 2 C 1 + C 2 C 1 + C 2 = 10 C 1 C 2 C 1 + C 2 C 1 + C 2 2 = 10 C 1 C 2 C 1 2 + C 2 2 - 8 C 1 C 2 = 0 dividing by C 1 2 C 2 C 1 2 - 8 C 2 C 1 + 1 = 0 Let C 2 C 1 = x x 2 - 8 x + 1 = 0 x = 8 ± 64 - 4 2 = 4 + 15 This question was Bonus in JEE Main 2021 exam because of incorrect data in original question.