A $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$
$300$
$600$
$900$
$450$
A parallel plate condenser with plate area $A$ and separation $d$ is filled with two dielectric materials as shown in the figure. The dielectric constants are $K_1$ and $K_2$ respectively. The capacitance will be
A thin square plate is placed in $x-y$ plane as shown in fig. such that is centre coinsides with origine it's charge density at point $(x, y)$ is $\sigma = \sigma _0xy$ (where $\sigma _0$ is constant). Find total charge on the plate.
Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+ q$ and $-q$. The potential difference between the centres of the two rings is
Three charges $4q,\,Q$ and $q$ are in a straight line in the position of $0$, $l/2$ and $l$ respectively. The resultant force on $q$ will be zero, if $Q = $
A solid spherical conducting shell has inner radius a and outer radius $2a$. At the center of the shell a point charge $+Q$ is located . What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?