The plates of a spherical capacitor have radii $37.0 \mathrm{mm}$ and $40.0 \mathrm{mm}.$ (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

In the given figure, a potential difference $V=75.0 \mathrm{V}$ is applied across a capacitor arrangement with capacitance $C_1=10.0 \mu \mathrm{F}, C_2=5.00 \mu \mathrm{F}$ and $C_3=15.0 \mu \mathrm{F}$. What is (a) charge $q_3,$ (b) potential difference $V_3$, (c) stored energy $U_3$ for capacitor $3,$ (d) $q_1,$ (e)$V_1,$ (f) $U_1$ for capacitor $1,$(g) $q_2$, (h) $V_2$ and (i) $U_2$ for capacitor $2?$

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?

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 $2.00 \mathrm{mm}$.

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 ?

In figure two parallel-plate capacitors (with air between the plates) are connected to a battery. Capacitor $1$ has a a plate area of $1.5 {\mathrm{cm}}^2$ and an electric field (between its plates) of magnitude $3500 \mathrm{V} {\mathrm{m}}^{-1}.$ Capacitor $2$ has a plate area of $0.70 {\mathrm{cm}}^2$ and an electric field of magnitude$1500 \mathrm{V} {\mathrm{m}}^{-1}$. (a) What is the total charge on the two capacitors? (b) If the first plate area is cut in half, does the total charge increase, decrease, or remain the same?