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.

Two sources of the current of equal emf are connected in series and have different internal resistances $R_1$ and $R_2\left(R_2>R_1\right)$. Find the external resistance $R$ at which the potential difference across the terminals of one of the sources (which one in particular?) becomes equal to zero.