In the circuit shown in the figure,for section $AB$,$C_1 = 1\ \mu F$,$C_2 = 2\ \mu F$,$E = 10\ V$,and the potential difference $V_A - V_B = -10\ V$. Find the charge on capacitor $C_1$.

Consider an infinite matrix of capacitors as shown in the figure. The effective capacitance between point $A$ and $B$ will be

$n$ identical capacitors are connected in parallel and charged to a potential $V$. Now,they are disconnected and reconnected in series. What will be the total energy and potential difference of the combination?

Consider two charged metallic spheres $S_{1}$ and $S_{2}$ of radii $R_{1}$ and $R_{2},$ respectively. The electric fields $E_{1}$ (on $S_{1}$) and $E_{2}$ (on $S_{2}$) on their surfaces are such that $E_{1} / E_{2} = R_{1} / R_{2}.$ Then the ratio $V_{1} / V_{2}$ of the electrostatic potentials on each sphere is:

$64$ drops,each having the capacity $C$ and potential $V$,are combined to form a big drop. If the charge on each small drop is $q$,then the charge on the big drop will be: (in $,q$)

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by the above two particles will be: