Q 12-02-138JEE MainJEE Main 2021 (26 Feb, Shift 1)Medium
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, $\frac{C_2}{C_1}$.
Answer: (A) $4+\sqrt{15}$
$C_1 + C_2 = 10\,\dfrac{C_1C_2}{C_1+C_2} \Rightarrow (C_1+C_2)^2 = 10C_1C_2$.
With $x = C_2/C_1$: $(1+x)^2 = 10x \Rightarrow x^2 - 8x + 1 = 0$
$$x = 4 \pm \sqrt{15}$$
Since $C_2 > C_1$, $x = 4 + \sqrt{15}$.
Solution by Sreeraj P, M.Sc Physics