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## electric current

### (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.

### (4 points)5. Series 27. Year - 4. Trianglular resistor

Determine the resistance of a triangle created out of resistive wires between clamps A a B, that you see in the picture. One side of the small triangle (of which the bigger triangle is composed of) has the resistance of $R_{0}.Neglect$ the resistance of the wires that led it there.

Karel was drawing triangles

### (4 points)2. Series 27. Year - P. Temelínská

Estimate how much nuclear fuel get used by an atomic powerplant to generate 1 MWh of electrical energy that people use at home. Compare it with the usage offuel in a thermal powerplant. Don't forget to think about all posible ways that energy gets lost.

**Bonus:** Include the energy that is required to transport the fuel into your solution.

Karel přemýšlel nad ČEZem.

### (4 points)1. Series 26. Year - 3. geography for physicists

Imagine that there are wires along all lines of latitude and longitude. These wires are connected at each point where they cross. Given that the resistance of one meter of this wire is $ρ$, calculate the resistance of this network between the nodes located at the North and South pole. Assume that the angular distance of neighboring lines of latitude/longitude is 15$°$.

**Bonus:** What would be the resistance between two nodes located on the equator and opposite of each other?

Honza dreamed of an around the world trip.