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
$\frac{1}{2}({V_1} + {V_2})$
$\frac{{{C_2}{V_1} + {C_1}{V_2}}}{{{C_1} + {C_2}}}$
$\frac{{{C_1}{V_1} + {C_2}{V_2}}}{{{C_1} + {C_2}}}$
$\frac{{{C_2}{V_1} - {C_1}{V_2}}}{{{C_1} + {C_2}}}$
Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $x -y$ coordinate system. Then
Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to distance equal to half their initial separation. The force of repulsion between them increases $4.5\,times$ in comparison with the initial value. The ratio of the initial charges of the balls is
For shown situation of two dipoles the nature of forces between them are
A capacitor $C = 100$ $ \mu F$ is connected to three resistors each of resistance $1$ $kW$ and a battery of emf $9$ $V$. The switch $S $ has been closed for long time so as to charge the capacitor. When switch $S $ is opened, the capacitor discharges with time constant.....$ms$
A particle of charge $Q$ and mass $m$ travels through a potential difference $V$ from rest. The final momentum of the particle is