Three capacitors of capacitances $25 \mu F, 30 \mu F$ and $45 \mu F$ are connected in parallel to a supply of $100 \ V$. Energy stored in the above combination is $E$. When these capacitors are connected in series to the same supply,the stored energy is $\frac{9}{x} E$. The value of $x$ is . . . . . . .

The figure shows a diagonal symmetric arrangement of capacitors and a battery. The potentials of the points $B$ and $D$ are:

Find the potential difference between points $A$ and $F$,and $F$ and $B$.

Four capacitors of capacitances $2 \mu F$,$3 \mu F$,$4 \mu F$,and $x \mu F$ are connected to a battery of emf $6 \text{ V}$ and of negligible internal resistance,as shown in the figure. If the ratio of the charges on $x \mu F$ and $4 \mu F$ capacitances is $\frac{3}{8}$,then the value of $x$ is

The charge on the $4\,\mu F$ capacitor in the given circuit is .... in $\mu C$.

In the circuit shown,initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1=10 \mu F$,$C_2=30 \mu F$,and $C_3=C_4=80 \mu F$.
Which of the statement$(s)$ is/are correct?
$(1)$ The key $S_1$ is kept closed for a long time such that capacitors are fully charged. Now key $S_2$ is closed. At this time,the instantaneous current across the $30 \Omega$ resistor (between points $P$ and $Q$) will be $0.2 A$.
$(2)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage difference between points $P$ and $Q$ will be $10 V$.
$(3)$ At time $t=0$,the key $S_1$ is closed,the instantaneous current in the closed circuit will be $25 mA$.
$(4)$ If key $S_1$ is kept closed for a long time such that capacitors are fully charged,the voltage across the capacitor $C_1$ will be $4 V$.