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In the given circuit, a charge of $+80 \ \mu C$ is given to the upper plate of the $4 \ \mu F$ capacitor. Then in the steady state, the charge on the upper plate of the $3 \ \mu F$ capacitor is :
A condenser of capacity ${C_1}$ is charged to a potential ${V_0}$. The electrostatic energy stored in it is ${U_0}$. It is connected to another uncharged condenser of capacity ${C_2}$ in parallel. The energy dissipated in the process is
In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S _1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C _2$. After some time, $S _2$ is released and then $S _3$ is pressed. After some time.
$(A)$ the charge on the upper plate of $C _1$ is $2 CV _0$
$(B)$ the charge on the upper plate of $C _1$ is $CV _0$
$(C)$ the charge on the upper plate of $C _2$ is $0$
$(D)$ the charge on the upper plate of $C _2$ is $- CV _0$
There are two equipotential surface as shown in figure. The distance between them is $r$. The charge of $-q\,$ coulomb is taken from the surface $A$ to $B$, the resultant work done will be
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is