Q 12-02-172JEE MainJEE Main 2019 (10 Apr, Shift 1)Easy
The charge $q$ versus voltage $V$ graphs for the series and parallel combinations of two given capacitors are straight lines through the origin. At $V = 10\ \text{V}$ one line gives $q = 500\ \mu\text{C}$ and the other gives $q = 80\ \mu\text{C}$. The capacitances are:
Answer: (D) $40\ \mu\text{F}$ and $10\ \mu\text{F}$
The slope $q/V$ is the capacitance. The steeper line is the parallel combination:
$$C_1 + C_2 = \frac{500}{10} = 50\ \mu\text{F},\qquad \frac{C_1C_2}{C_1+C_2} = \frac{80}{10} = 8\ \mu\text{F}$$
So $C_1C_2 = 400$, and $C_1, C_2$ are roots of $C^2 - 50C + 400 = 0$: $40\ \mu\text{F}$ and $10\ \mu\text{F}$.
Solution by Sreeraj P, M.Sc Physics