A capacitor of capacitance $C$ is charged to a potential $V$ and disconnected from the battery. Now, if the space between the plates is completely filled with a substance of dielectric constant $K$, the final charge and the final potential on the capacitor are respectively.

For the displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ to be $150 \mu \mathrm{~A}$, the potential difference across the plates of the capacitor has to vary at the rate of

A capacitor of capacitance $(4.0 \pm 0.2) \mu \mathrm{F}$ is charged to a potential of $(10.0 \pm 0 \mathrm{l}) \mathrm{V}$. The charge on the capacitor is

Two capacitors of capacitances $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ can separately withstand potentials of 6 kV and 4 kV respectively. The total potential, they together can withstand when they are connected in series is

A $10 \mu \mathrm{~F}$ capacitor is charged by a 100 V battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu \mathrm{~F}$. During this process, the electrostatic energy lost by the first capacitor is

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is $C_1$. If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is $C_2$. If in both cases, the dielectric is placed parallel to the plated of the capacitor, then $C_1: C_2=$

The natural frequency of an $L-C$ circuit is 120 kHz . When the capacitor in the circuit is totally filled dielectric material, the natural frequency of the circuit decreases by 20 kHz . Dielectric constant of material is

Three capacitors of capacitances $10 \mu \mathrm{~F}, 5 \mu \mathrm{~F}$ and $20 \mu \mathrm{~F}$ are connected in series with a 14 V DC supply. The charge on $5 \mu \mathrm{~F}$ capacitor is