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This is the problem of the 8$^\mathrm{th}$ International Experimental Physics Olympiad (EPO). The task of the EPO8 is to determine Plank constant $\hbar=h/2\pi$ using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items -- they are instructive for physics education in general.Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best., Comment: 27 pages (10 main text), 11 figures, 3 tables, 18 references, 1 appendix of scanned solution (16 pages); latex source files in Bulgarian and Macedonian languages included as auxiliary files. arXiv admin note: text overlap with arXiv:1912.07368

For the need of measurements focused in condensed matter physics and especially Bernoulli effect in superconductors we have developed an active resonator with dual operational amplifiers. A tunable high-Q resonator is performed in the schematics of the the General Impedance Converter (GIC). In the framework of frequency dependent open-loop gain of operational amplifiers, a general formula of the frequency dependence of the impedance of GIC is derived. The explicit formulas for the resonance frequency and Q-factor include as immanent parameter the crossover frequency of the operational amplifier. Voltage measurements of GIC with a lock-in amplifier perfectly agree with the derived formulas. A table reveals that electrometer operational amplifiers are the best choice to build the described resonator., Comment: a new formulae for the Q-factor expressed by resonance frequency, dominant frequency and cross-over frequency, a general guide with a table for selection of appropriate operational amplifiers, 9 new (30 total) references, Fig. 6 in appendix B corrected

Heat capacities at fixed volume and pressure as a function of the degree of ionization are graphically depicted as functions of reciprocal temperature and ionization degree. The polytropic index is calculated as a function of the same variables; as it is not constant a partially ionized plasma can be only approximately polytropic fluid. In parallel, it is launched the idea that Alfv\'en waves can be used to heat the plasma in a propulsion jet with magnetic nozzle., Comment: 2 pages, 3 figures

The time dependent master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, "Analysis of Problems in Dynamics by Electronic Circuits", Proc. of the I.R.E., Vol. 35, pp. 444--452, (1947)] is recovered as necessary tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage $U_0(t)$ and the difference between the input voltages ($U_{+}(t)$ and $U_{-}(t)$). The crossover frequency $f_0$ is represented the time constant $\tau_{_0}$ of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications without citations of time dependent equation. A simple circuit for determination of $f_0$ is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is a useful technique implicitly included in the contemporary software. The frequency dependent formulae for the amplification coefficient of inverting and non-inverting amplifiers are given for the case of non-zero conductivity between the inputs of the operational amplifiers., Comment: 14 pages, 9 figures, 3 appendices. arXiv admin note: text overlap with arXiv:1703.05224

We re-derive the Nyquist theorem and Callen-Welton fluctuation-dissipation theorem (FDT) as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of Waterston-Herapath equipartition theorem., Comment: 6 pages, 1 figure

A simple experiment for the electron charge $q_e$ measurement is described. The experimental set-up contains standard electronic equipment only and can be built in every high-school lab all around the world with pocket money budget for several days. It is concluded that it is time such a practice to be included in the regular high-school education. The achieved 13\% accuracy is comparable to the best student university labs. The measurement is based on Schottky noise generated by a photodiode. Using the criterion dollar per accuracy for the electron charge $q_e$ measurement, this definitely is the world's best educational experiment. An industrial replica can be easily sold across the globe., Comment: 10 pages, 9 figures, 3 tables, last version corresponds to the published version in Eur. J. Phys, Eq. (15-17) have been corrected and minor typographical improvements have been made

A new experimental set-up for Boltzmann constant measurement is described. Statistically averaged square of voltage $\left$ is measured for different capacitances $C$. Boltzmann constant is determined by the equipartition theorem $C\left=k_{_\mathrm{B}}T$. For fixed capacitance, voltages could be measured for different temperatures. The set-up consists of low-noise high frequency operational amplifiers ADA4898-2. An instrumental amplifier is followed by an inverting amplifier, square of the voltage is created by an analog multiplier AD633 and finally the averaged signal is measured by a multimeter., Comment: 14 pages, 8 figures, 3 tables, 2 appendices