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Electrodynamics Learning Material
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In this Physics tutorial, you will learn:

  • How do we measure the current in a circuit?
  • How do we measure the potential difference in a circuit?
  • What is superconductivity?
  • What is the condition for a material to become a superconductor?
  • How is the current produced in liquids?
  • What is electrolysis?
  • What does the Faraday's Law of Electrolysis say?
  • How to calculate the amount of substance produced through electrolysis?
  • How the current is produced in gases?


How do we measure the value of current and voltage in a circuit? Do you know the procedure of terminals connection? Explain.

Do you think there exists any electric current in liquids and gases?

Is it possible to use any material that has no resistance? Have you ever heard about superconductors?

In Chemistry, you have learned about electrolysis. Is it applicable in Physics? In which way?

This tutorial contains a number of apparently non-related phenomena which when considered individually cannot form a specific tutorial as they are very short. Therefore, they are grouped in this particular topic which comes after all the other electric-related phenomena are discussed, so the reader will not have any trouble in understanding them.

Measurement of Current and Voltage

In tutorial 15.4 "Electric Circuits. Series and Parallel Circuits. Short Circuits" we have shortly explained what ammeter and voltmeter are used for. Thus, we have explained that ammeter is used to measure the value of electric current in the circuit. It is connected in series with the operating appliance in the circuit. On the other hand, a voltmeter is used to measure the value of potential difference in the circuit. It is connected in parallel to the operating appliance in the circuit.

But why this is so? Why ammeter is connected in series to appliances and voltmeter is parallel to them? Let's explain the logic of this setup.

a. Ammeter

Since ammeter is used to measure the current in the circuit, it can be placed at any position of the conductor since the current is the same at every point of a circuit branch. An ammeter has a very low internal resistance because and therefore, the potential difference across its terminals is negligible, otherwise this (a high resistance) would affect the value of potential difference in the operating device. This would result in wrong values not only for the potential difference but also for electric power, efficiency and so on.

The figure below shows the connection of an ammeter in a circuit in both real and simplified view (in symbols).

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b. Voltmeter

Since voltmeter is used to measure the potential difference across the terminals of a circuit element, it must be connected in parallel to it that is one wire of voltmeter is connected before the appliance and the other wire after the appliance. This is because the voltmeter has a very high resistance in order to affect as less as possible the value of current flowing in the circuit. In other words, a very high resistance allows only a negligible amount of current to flow through the voltmeter. Look at the figure.

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Example 1

What are the readings of ammeter and voltmeter in the circuit below if the resistance of battery is 1 Ω and that of the conducting wire is 0.5 Ω?

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Solution 1

The ammeter measures the current in the main branch (Itot) while the voltmeter measures the potential difference ΔV in the parallel branch.

First, we must calculate the equivalent resistance in the parallel branch. We have

1/Req = 1/R1 + 1/R2
= 1/2 + 1/6
= 2 + 1/6
= 3/6
= 1/2

Thus, Req = 2 Ω.

The total resistance in the circuit is

Rtot = Req + Rwire + rbattery
= 2Ω + 0.5Ω + 1Ω
= 3.5Ω

The reading of ammeter that shows the current in the main branch therefore is

Itot = ε/Rtot
= 21 V/3.5 Ω
= 6 A

As for the reading of voltmeter, it shows the potential difference ΔV in the parallel branch, which is calculated by

ΔV = ε - I ∙ Rw - I ∙ r
= 21V - 6A ∙ 0.5Ω - 6A ∙ 1Ω
= 21V - 3V - 6V
= 12V

Therefore, the ammeter reads 6A and the voltmeter reads 12V.


A superconductor is a material whose resistance is very low, close to zero. As discussed in tutorial 15.2, resistance of material largely depends on its temperature, i.e. higher the temperature of material, higher its resistance. Given this, a material obviously must behave as a superconductor at very low temperatures (close to the absolute zero).

A Dutch scientist called H. K. Ones was the first who discovered the phenomenon of superconductivity in 1911. When cooling down mercury at very low temperature, he realized that the resistance of mercury became almost zero. During the observations, he noticed that at 4.2 K (-268.960 C) the resistance of mercury suddenly became zero.

Other substances are able to show superconductive properties as well. This occurs when temperature decreases below a threshold value, known as the transition temperature, TC. The table below shows some superconductors along with the corresponding transition temperatures.

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Superconductivity occurs due to the position of atoms in molecules in certain combinations, which cause enormous free spaces between neighbouring atoms. As a result, electrons move unopposed throughout the material.

The other advantage of a superconductor besides the high efficiency of energy transmission is the long lasting current flow when the source stops supplying the circuit.

In the future, there is a lot of possibility to improve the technology of superconductor production. If scientists are able to produce a strong superconductor with a higher transition temperature than the actual materials, this will bring a revolution in technology, as motors and generators dimensions would be four to five times smaller than the actual ones. In addition, computers would be much faster, electricity transmission would be cheaper and more efficient, electromagnets would be stronger and so on.

Electric Current in Liquids

In tutorial 15.4 "Electric Circuits. Series and Parallel Circuits. Short Circuits", we have explained how a wet cell works. A wet cell is an example of the existence of electric current in liquids.

Pure water does not conduct electricity. Therefore, we must add some acidic element in it. The cheapest and most accessible material for this purpose is the table salt.

As explained earlier, the liquid acid is known as electrolyte and the two metal plates (usually made of zinc and copper) are known as electrodes - zinc electrode that is connected to the positive terminal of battery is called anode while the copper electrode connected to the negative terminal of battery is called cathode. The current inside the electrolyte is conducted by the positive and negative ions (electricity carriers) while electrons conduct the electricity through the conducting wires outside the electrolyte. The figure below shows how the electricity produced by a wet cell flows when table salt (NaCl) is used as an electrolyte.

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The zinc plate (anode) gains electrons (it becomes negatively charged) while the copper plate releases them. These electrons travel through the electrolyte in the ionic form, i.e. some molecules of the electrolyte dissolve and become positive and negative ions. This process maintains a steady flow of current in the circuit.

The process of charges flow through an electrolyte is called electrolysis.

Faraday's Law for Electrolysis

Let's consider again the wet cell discussed in the previous paragraph. When some table salt is poured in water, the Na + and Cl- ions dissolve in water. The Na + ions start to move towards the copper plate (cathode) taking away an electron from it. The Cl- ions do the opposite thing, i.e. they move towards the zinc plate (anode) and become neutral there. As a result, an electric current flows inside the electrolyte and the copper electrode is covered by a zinc layer. In technology, such a process is known as electroplating and it is used to protect metals from corrosion, oxidation or for decoration purpose.

Michael Faraday introduced an equation which represents the relationship between the amount (mass) m of substance decomposed to the anode (deposited in the cathode) and the current I flowing through the electrolyte. This equation, known as the Faraday's Law for Electrolysis is

m = k ∙ Q
= k ∙ I ∙ t

where k is a constant known as the electrochemical constant of electrolysis. It has the unit of [kg/A ∙ s]. I shows the current and t the time during which the electrolysis takes place.

The acid added in water is not the only material that is decomposed. Water also decomposes in two separate elements: hydrogen and oxygen. The salty water simply increases the conductive ability of water. The chemical reaction that takes place during the water electrolysis is

H2 O ⟶ H2 + 1/2 O2

If we consider the two gases produced during the electrolysis as ideal gases (all ideal gases have the same volume for the same number of particles), we can see from the above reaction formula that the volume of hydrogen collected in a tube placed on the cathode is twice the volume of oxygen collected in the tube on the anode.

The process of electrolysis is used to obtain pure hydrogen or oxygen from water decomposition.

Example 2

How much time is needed to obtain 2 kg of copper during an electrolysis process when a 5A current flows through the electrolyte? Take kcopper = 3.3 × 10-7 kg/A ∙ s.

Solution 2


m = 2 kg
I = 5 A
k = 3.3 × 10-7 kg/A ∙ s
t = ?

From the Faraday's Law of Electrolysis

m = k ∙ I ∙ t

we obtain from the time t after rearranging the above equation

t = m/k ∙ I
= 2 kg/3.3 × 10-7 kg/A ∙ s ∙ (5A)
= 0.1212 × 107 s
= 1 212 121 s

When converted into hours (1h = 3600s) we obtain

t = 336.7 hours

or about 14 days. This result means the process of electrolysis is relatively slow.

Electric Current in Gases

In normal conditions, gases are insulators. When a gas is heated, the kinetic energy of its molecules increases. When this kinetic energy exceeds the binding energy (i.e. the energy that keep electrons bound with the atoms), electrons escape from atoms and as a result, atoms begin to ionise. If the temperature of gas is high enough, the gas becomes a mixture of positive ions and free electrons. Such a state is known as plasma and it represents the fourth state of matter besides solid, liquid and gas states we have explained earlier. A material in plasma state is a good conductor of electricity as it contains a lot of free charges.

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Heating the gas is not the only method to obtain free charges. Electromagnetic radiation is another factor that produces electric current in metals due to ionization of gas particles, as shown in the figure below.

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A third factor that can cause gas ionization (and therefore an electric current) is a high potential difference produced due to the existence of an electric field inside the gas. For this, a power source such as a battery is needed. Electrons accelerate due to the electric field and gain a high kinetic energy over a small distance. When electrons strike the gas atoms, they pull out new electrons from atoms turning them into positive ions. This kind of ionization is called discharge by self-ionisers. Look at the figure below.

Physics Tutorials: This image provides visual information for the physics tutorial Miscellaneous

The phenomenon of discharge by self-ionisation is used to construct light bulbs and self-illuminating structures such as billboards, light tubes etc.

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