The circuit shown in is made of a homogeneous wire of constant cross section.

Find the ratio $\frac{Q_{12}}{Q_{34}}$ of the amounts of heat liberated per unit time in conductors $1-2$ and $3-4$.

Determine the strength $E$ of the electric field at the centre of a hemisphere produced by charges uniformly distributed with a density, $\sigma$ over the surface of this hemisphere.

The strength of the electric field produced by charges uniformly distributed over the surface of a hemisphere at its centre $O$ is $E_0$. A part of the surface is isolated from

this hemisphere by two planes passing through the same diameter and forming an angle $\alpha$ with each other determine the electric field strength $E$ produced at the same point $O$ by the charges located on the isolated surface (on the "mericarp").

The voltage between the anode and the cathode of a vacuum-tube diode is $U$ and the anode current is $I$.

Determine the mean pressure $p_{\mathrm{m}}$ of electrons on the anode surface of area $S$.

across the capacitor plates varies as shown in the figure Plot the time dependence of voltage across the clamps $CD$.

An electric circuit consists of a current source of emf $\epsilon$ and internal resistance $r$, and two resistors connected in parallel to the source (Fig.). The resistance $R_1$ of one resistor remains unchanged, while the resistance $R_2$ of the other resistor can be chosen so that the power liberated in this resistor is maximum.

Determine the value of $R_2$ corresponding to the maximum power.

A quadratic undeformable superconducting loop of mass $m$ and side $a$ lies in a horizontal plane in a nonuniform magnetic field whose induction varies in space according to the law $B_x=-\alpha x,B_y=0,B_z=\alpha z+B_0$. The inductance of the loop is $L$. At the initial moment, the centre of the loop coincides with the origin $O$, and its sides are parallel to the $x$ and $y$-axes. The current in the loop is zero, and it is released.

How will it move and where will it be in time $t$ after the beginning of motion?

Two long cylindrical coils with uniform windings of the same length and nearly the same radius have inductances $L_1$ and $L_2$. The coils are coaxially inserted into each other and connected to a current source as shown in. The directions of the current in the circuit and in the turns are shown by arrows.

Determine the inductance $L$ of such a composite coil.

A winch is driven by an electric motor with a separate excitation and fed from a battery of emf $\epsilon =300 \mathrm{V}$. The rope and the hook of the winch rise at a velocity $v_1=4{\mathrm{ms}}^{-1}$ without a load and at a velocity $v_2=1{\mathrm{ms}}^{-1}$ with a load of mass $m=10\mathrm{kg}$.

Determine the velocity $v^{\text{'}}$ of the load and its mass $m^{\text{'}}$ for which the winch has the maximum power, neglecting the mass of the rope and the hook.