A dielectric material is to fill the space in a capacitor. Initially, with only air in place, the capacitance is $8.0 \mathrm{pF}$. With the dielectric material in place, the capacitor should store $3.2 \mu \mathrm{J}$ at a maximum potential difference of $350.8 \mathrm{V}$ . (a) What dielectric constant is required? (b) Of the materials in Table which material should be used?

Material	Dielectric constant
Air	$1$
Glass	$14.5$
Porcelain	$6.5$
Quartz	$5$
Vinylite	$7.5$

 

In Fig., how much charge is stored on the parallel-plate capacitors by the$10.0 \mathrm{V}$ battery? One is filled with air, and the other is filled with a dielectric for which $\kappa =3.00;$ both capacitors have a plate area of $5.00\times {10}^{-3} {\mathrm{m}}^2$ and a plate separation of $2.00 \mathrm{mm}$.

Figure shows a parallel plate capacitor with a plate area $A=5.56 {\mathrm{cm}}^2$ and separation $\mathrm{d}=5.56 \mathrm{mm}$. The left half of the gap is filled with material of dielectric constant${\kappa }_1=7.00;$ the right half is filled with material of dielectric constant ${\kappa }_2=10.0.$What is the capacitance?

In Fig., ${\mathrm{C}}_1=10.0 \mathrm{\mu F}$,$C_2=20.0 \mu \mathrm{F}$ and $C_3=5.00$ $\mu \mathrm{F}$. If no capacitor can withstand a potential difference of more than $100 \mathrm{V}$ without failure, what are (a) the magnitude of the maximum potential difference that can exist between points $A$ and $B$ and (b) the maximum energy that can be stored in the three-capacitor arrangement ?