Intially, switch $S$ is connected to position $1$ for a long time shown in figure. The net amount of heat generated in the circuit after it is shifted to position $2$ is
$\frac{C}{2}\left( {{\varepsilon _1} + {\varepsilon _2}} \right){\varepsilon _2}$
$C\left( {{\varepsilon _1} + {\varepsilon _2}} \right){\varepsilon _2}$
$\frac{C}{2}{\left( {{\varepsilon _1} + {\varepsilon _2}} \right)^2}$
$C{\left( {{\varepsilon _1} + {\varepsilon _2}} \right)^2}$
Two insulated metallic spheres of $3\,\mu F$ and $5\,\mu F$ capacitances are charged to $300\, V$ and $500\, V$ respectively. The energy loss, when they are connected by a wire is
A parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, volt$ battery. Then the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ and the plates are maintained in connection with the battery, is
A parallel plate capacitor is made of two square parallel plates of area $A$ , and separated by a distance $d < < \sqrt A $ . The capacitor is connected to a battery with potential $V$ and allowed to fully charge. The battery is then disconnected. A square metal conducting slab also with area $A$ but thickness $\frac {d}{2}$ is then fully inserted between the plates, so that it is always parallel to the plates. How much work has been done on the metal slab by external agent while it is being inserted?
$27$ similar drops of mercury are maintained at $10 \,V$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.
$A$ $2$ $\mu F$ 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?......$\mu J$