At what value of the resistance $R_{\mathrm{x}}$, in the circuit shown in the figure, will the total resistance between points $A$ and $B$ be independent of the number of cells?

Figure shows an infinite circuit formed by the repetition of the same link, consisting of resistances $R_1=4.0 \mathrm{\Omega }$ and $R_2=3.0 \mathrm{\Omega }$. Find the resistance of this circuit between points $A$and $B$.

The gap between the plates of a parallel-plate capacitor is filled with glass of resistivity $\rho =100 \mathrm{G\Omega } \mathrm{m}$. The capacitance of the capacitor equals $C=4.0 \mathrm{nF}$. Find the leakage current of the capacitor, when a voltage $V=2.0 \mathrm{kV}$ is applied to it. (Permittivity of vacuum, ${\epsilon }_0=0.885\times {10}^{-11} \mathrm{F} {\mathrm{m}}^{-1}$, $\epsilon =$ Dielectric constant for glass $=6$)

A capacitor is filled with dielectric of permittivity, $\epsilon =2.1$, loses half the charge acquired during a time interval, $\tau =3.0 \min$. Assuming the charge to leak only through the dielectric filler, calculate its resistivity (permittivity of vacuum, ${\epsilon }_0=0.885\times {10}^{-11} \mathrm{F} {\mathrm{m}}^{-1}$).

A circuit consists of a source of a constant emf $\xi$ and a resistance $R$ and a capacitor with capacitance $C$ connected in series. The internal resistance of the source is negligible. At a moment $t=0$, the capacitance of the capacitor is abruptly decreased $\eta$-fold. Find the current flowing through the circuit as a function of time $t$.

An ammeter and a voltmeter are connected in series to a battery with an emf $\xi =6.0 \mathrm{V}$. When a certain resistance is connected in parallel with the voltmeter, the readings of the latter decrease $\eta =2.0$ times, whereas the readings of the ammeter increase the same number of times. Find the voltmeter readings after the connection of the resistance.