Exercise-3

A parallel- plate capacitor of area $\mathrm{A},$plate separation $\mathrm{d}$ and capacitance $\mathrm{C}$ is filled with four dielectric materials having dielectric constant ${\mathrm{k}}_1, {\mathrm{k}}_2, {\mathrm{k}}_3$ and ${\mathrm{k}}_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance $\mathrm{C}$ in this capacitor, then its dielectric constant $\mathrm{k}$ is given by 

In the given circuit, charge $Q_2$ on the $2\mu F$ capacitor changes as $C$ is varied from $1\mu F$ to $3\mu F.$ $Q_2$ as a function of ${{}^{\text{'}}C}^{\text{'}}$ is given properly by: (figures are drawn symmetrically and are not to scale)

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4\mu F$ and $9\mu F$ capacitors), at a point distance $30 \mathrm{m}$ from it, would equal :

A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1,{ K}_2,$ $K_3,{ K}_4$ arranged as shown in the figure. The effective dielectric constant $K$ will be-

A parallel plate capacitor is of area $6{ \mathrm{cm}}^2$ and a separation $3 \mathrm{mm}.$ The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_1=10,{ K}_2=12$ and $K_3=14.$ The dielectric constant of a material which when fully inserted in the above capacitor, gives the same capacitance would be:

Seven capacitors, each of capacitance $2 \mathrm{\mu F}$ are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right) \mu \mathrm{F}.$ Which of the combinations, shown in figures below, will achieve the desired results?

In the figure shown below, the charge on the left plate of the $10 \mathrm{\mu F}$ capacitor is $-30 \mathrm{\mu C}.$ The charge on the right plate of the $6 \mathrm{\mu F}$ capacitor is:

In the figure shown, after the switch $S$ is turned position $A$ to position $B,$ the energy dissipated in the circuit in terms of capacitance $C$ and total charge $Q$ is: