A parallel plate capacitor with air between the plates has a capacitance of  $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$

A charg $Q$ is divided into two parts $q$ and $Q-q$ and separated by a distance $R$ . The force of repulsion between them will be maximum when

A charge $Q$ is divided into two parts of $q$ and $Q - q$. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

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

What is the equivalent capacitance of the system of capacitors between $A$ and $B$ :-

A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$ . Another capacitor of capacitance $2C$ is similarly charged to a potential difference $2V$ . The charging battery is now disconnected and the capacitors are connect in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of  the configuration is