A cylindrical capacitor is filled with two cylindrical layers of dielectric with permittivities ${\epsilon }_1$ and ${\epsilon }_2.$ The inside radii of the layers are equal to $R_1$ and $R_2 \left(R_2>R_1\right)$. The maximum permissible values of electric field strength are equal to $E_{1\mathrm{m}}$ and $E_{2\mathrm{m}}$, for these dielectrics. At what relationship between ${\epsilon }_1{R}_1$ and $E_{\mathrm{m}}$, will the voltage increase result in the field strength reaching the breakdown value, for both dielectrics simultaneously?

There is a double-layer cylindrical capacitor whose parameters are shown in the figure. The breakdown field strength values for these dielectrics are equal to $E_1$ and $E_2$, respectively. What is the breakdown voltage of this capacitor, if ${\epsilon }_1{R}_1{E}_1<{\epsilon }_2{R}_2{E}_2$?

Two long straight wires with equal cross-sectional radii $a$ are located parallel to each other in air. The distance between their axes equals $b$. Find the mutual capacitance of the wires per unit length, under the condition $b\gg a$.

Find the capacitance of a system of identical capacitors between points $A$ and $B$, as shown in the figures.
(a)
(b)

Four identical metal plates are located in air at equal distances $d$ from one another. The area of each plate is equal to $S$. Find the capacitance of the system between points $A$ and $B$, if the plates are interconnected as shown.
(a) 
(b)

Find the potential difference between points $A$ and $B$ of the system, shown in the figure, if the emf is equal to $\epsilon =110 \mathrm{V}$ and the capacitance ratio, $\frac{C_2}{C_1}=\eta =2.0$.

Find the capacitance of an infinite circuit formed by the repetition of the same link, consisting of two identical capacitors each with capacitance $C$ (figure).