If the distance between the plates of a capacitor having capacity $C$ and charge $Q$ is doubled then work done will be
$\frac{{{Q^2}}}{{4C}}$
$\frac{{{Q^2}}}{{2C}}$
$\frac{{{Q^2}}}{{C}}$
$\frac{{{2Q^2}}}{{C}}$
A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R$ $( R > r ) .$ If the surface charge densities on the two shells are equal, the electric potential at the common centre is
The work done in placing a charge of $8 \times 10^{-18}$ coulomb on a condenser of capacity $100\, micro-farad$ is
A network of four capacitors of capacity equal to $C_1 = C,$ $C_2 = 2C,$ $C_3 = 3C$ and $C_4 = 4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is
Find capacitance across $AB$
Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of a $(x, y)$ coordinate system. Then