Figure shows charge (q) versus voltage (V) graph for series and… | JEE Main 2019 (10 Apr, Shift 1)

Q75JEE Main 2019 · 10 APR · SHIFT 1Medium

Combination of Capacitors

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are:

Show answer and solution

Answer: (a)

Larger slope is parallel: $C_p = \frac{500}{10} = 50\ \mu\text{F}$ ; smaller is series: $C_s = \frac{80}{10} = 8\ \mu\text{F}$ .
$C_1 + C_2 = 50$ and $\frac{C_1C_2}{C_1+C_2} = 8 \Rightarrow C_1C_2 = 400$ .
So $C_1, C_2$ are roots of $x^2 - 50x + 400 = 0$ : $40$ and $10$ .
So the answer is (a) $40\ \mu\text{F}$ and $10\ \mu\text{F}$ .

More questions on Combination of Capacitors

Which of the following combinations of 7 identical capacitors each of 2 gives a resultant…MHT CET 2019 (2 May, Shift 1)
Seven capacitors, each of capacitance 2 μ F, are to be connected in a configuration to…JEE Main 2019 (11 Jan, Shift 2)
In the given circuit, the charge on 4 μ F capacitor will be:JEE Main 2019 (12 Apr, Shift 2)
In the circuit shown, find C if the effective capacitance of the whole circuit is to be…JEE Main 2019 (12 Jan, Shift 2)
In the figure shown below, the charge on the left plate of the 10 μ F capacitor is –30 μ…JEE Main 2019 (11 Jan, Shift 1)
The equivalent capacitance between A and B in the circuit given below, is:JEE Main 2018 (15 Apr, Shift 1)
A capacitance of 2 μ F is required in an electrical circuit across a potential difference…JEE Main 2017
Three capacitors each of 4 μ F are to be connected in such a way that the effective…JEE Main 2016 (9 Apr, Shift 1)