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## electric current

### (7 points)4. Series 31. Year - 4. solve it yourself

We have a black box with three outputs (A, B, and C). We know that it consists of $n$ resistors with the same resistance but we don't know the circuit diagram. So we measure the resistance between each pair of outputs $R\_{AB} = 3 \mathrm{\Omega }$, $R\_{BC} = 5 \mathrm{\Omega }$ a $R\_{CA} = 6 \mathrm{\Omega }$. Your task is to find the minimum possible $n$ and calculate the corresponding resistance of one resistor.

Matěj solved it quickly.

### (6 points)0. Series 31. Year - 3.

We are sorry. This type of task is not translated to English.

### (3 points)2. Series 30. Year - 2. ultra high temperature superconducticvity

Many types of materials, mostly metals, have increasing dependence of resistivity on temperature. However, there are semiconductors or graphite which show a decreasing dependence. And you have also probably heard about superconductivity, the natural phenomenon when a cooled material shows almost no electrical resistance and becomes a perfect conductor. Our current state of knowledge says that the temperature of a superconductor must be well below room temperature, but let's assume that the equation defining the resistance is $R=$ R_{0} (1 + αΔt), where $R_{0}is$ the resistance at room temperature, $αis$ the temperature coefficient of resistance and $Δt$ is the temperature difference with respect to room temperature, and the equation holds for any temperature. Using this equation and coefficients $α_{C}=-0.5\cdot 10^{-3}K^{-1}$ for graphite and $α_{Si}=-75\cdot 10^{-3}K^{-1}$ for silicon, we obtain zero resistance for high temperatures. Determine these two temperatures and explain why the superconducting phenomenon does not work this way, i.e. neither carbon nor silicon are superconductors at high temperatures.

Karel se inspiroval nekonstantními konstantami.

### (4 points)6. Series 29. Year - 4. Fire in the hole

Neutral particle beams are used in various fusion devices to heat up plasma. In a device like that, ions of deuterium are accelerated to high energy before they are neutralized, keeping almost the initial speed. Particles coming out of the neutralizer of the COMPASS tokamak have energy 40 keV and the current in the beam just before the neutralization is 12 A. What is the force acting on the beam generator? What is its power?

### (2 points)5. Series 29. Year - 1. let it flow

Thin wire with resistance $R=100mΩ$ and length $l=1\;\mathrm{m}$, that is connected to the source of DC with voltage $U=3V$, contains in its volume $N=10^{22}$ free electrons, which contribute to the electric current. Determine what is the average speed (more accurately net velocity) of these electrons in the wire.

### (7 points)5. Series 29. Year - E. photographic

With the aid of a digital camera measure the frequency of the AC voltage in the electrical grid. A smart phone with an app supporting manual shutter speed should be a sufficient tool.

### (2 points)3. Series 29. Year - 2. alchemist's apprentice

The young alchemist George has learnt to measure electrochemical equivalents. He measured quite precisely the electrochemical equivalent $A=(6.74±0.01)\cdot 10^{-7}\;\mathrm{kg}\cdot C^{-1}$ of an unknown sample. How can he determine what substance was his sample made of?

### (2 points)1. Series 29. Year - 1. densifying Hofmann

During the electrolysis in a Hofmann voltameter the electolyte is a soluton of sulfuric acid in water. The mass of the acid in the solution is practicaly constant but as the name says the water slowly dissolves into hydrogen and oxygen. So the concentration of the acid in the solution rises. How long will take for the mass fraction of the acid in the solution to rise to twice the original amount if there was a current of $I=1A$ passing through the solution, the original mass fraction of the acid in the solution was $w_{0}=5%$ and the volume of the solution in the container was$V_{0}=2l?$

Karel was thinking about electrolysis again.

### (2 points)4. Series 28. Year - 1. square resistance

How does the eletric resistance of a square depend on the length of its side $a?$ All the squares that we are interested in are conductors made of a thin of a thickness $h$ and a resistivity $ρ$. We are interested in the resistance between the opposite sides of a square.

Karel was inspired at the fair of physics teacher's ideas.

### (8 points)1. Series 28. Year - E. charged potato

Measure the load characteristic of a potato as a source of electric voltage with electrodes made from different metals.

Karel was thinking about easy experiments.