$A$ parallel combination of three capacitors of capacities $2C$,$C$,and $C/2$ is connected across a $10 \ V$ battery. All the capacitors are fully charged to charges $Q_1$,$Q_2$,and $Q_3$ respectively. The ratio $Q_1: Q_2: Q_3$ is

The equivalent capacitance between points $X$ and $Y$ in the given figure is . . . . . . . (in $\mu F$)

Two capacitors of capacitance $2\ \mu F$ and $3\ \mu F$ are joined in series. The outer plate of the first capacitor is at $1000\ V$ and the outer plate of the second capacitor is earthed (grounded). The potential on the inner plates of each capacitor will be: (in $V$)

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 $\mu F.$

Two capacitors of capacities $2 \mu F$ and $4 \mu F$ are connected in parallel. $A$ third capacitor of $6 \mu F$ capacity is connected in series with this combination. $A$ battery of $12 \text{ V}$ is connected across this combination. The charge on the $2 \mu F$ capacitor is: (in $\mu C$)

The equivalent capacitance between $A$ and $B$ is.......$\mu \,F$