Q 12-02-190JEE MainJEE Main 2019 (12 Jan, Shift 2)Medium
In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5\ \mu$F. All values in the circuit are in $\mu$F.
Answer: (C) $\dfrac{7}{11}\ \mu$F
Right part: the two $2\ \mu$F capacitors in series give $1\ \mu$F, in parallel with $1\ \mu$F: $2\ \mu$F. In series with the top $2\ \mu$F: $1\ \mu$F.
Left column: $2\ \mu$F in series with $(2 + 2) = 4\ \mu$F gives $\dfrac43\ \mu$F.
Between X and B these two paths are in parallel: $1 + \dfrac43 = \dfrac73\ \mu$F. In series with $C$:
$$\frac1C + \frac37 = \frac{1}{0.5} = 2 \Rightarrow \frac1C = \frac{11}{7} \Rightarrow C = \frac{7}{11}\ \mu\text{F}$$
Solution by Sreeraj P, M.Sc Physics