Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be
$\frac{1}{2}({V_1} + {V_2})$
$\frac{{{C_2}{V_1} + {C_1}{V_2}}}{{{C_1} + {C_2}}}$
$\frac{{{C_1}{V_1} + {C_2}{V_2}}}{{{C_1} + {C_2}}}$
$\frac{{{C_2}{V_1} - {C_1}{V_2}}}{{{C_1} + {C_2}}}$
If there are $n$ capacitors in parallel connected to $V \,volt$ source, then the energy stored is equal to
Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is
If the charge on a capacitor is increased by $2\, C$ the energy stored in it increases by $21\%$. The original charge on the capacitor (in coulomb) is
The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$ where $r$ is the distance from the centre $a,\,b$ are constants. Then the charge density inside the ball is
Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame in $xy$ plane as shown in figure. The plane of the frame is perpendicular to $z-$ axis. If a $-ve$ point charges is placed at a distance $z$ away from the above frame $(z << L)$ then