$A$ circuit is shown in the figure for which $C_1=(3 \pm 0.011) \mu F$,$C_2=(5 \pm 0.01) \mu F$,and $C_3=(1 \pm 0.01) \mu F$. If $C$ is the equivalent capacitance across $AB$,then $C$ is given by:

$N$ identical spherical drops,each charged to the same potential $V$,are combined to form a single big drop. What will be the potential of the new big drop?

Four capacitors are connected to a battery as shown in the circuit. The ratio of charges on capacitors $C_2$ and $C_4$ is (Assume $C_1 = 1 \mu F, C_2 = 2 \mu F, C_3 = 3 \mu F, C_4 = 4 \mu F$ and the battery voltage $V = 10 \ V$ connected across the combination).

The figure shows a diagonal symmetric arrangement of capacitors and a battery. Identify the correct statements.

Each plate of a parallel plate capacitor has a charge $q$ on it. The capacitor is now connected to a battery. Now,

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 $4 V$.