Having connected the current source to the conducting circuit, using a multimeter, measure the potential difference (voltage) at the control points. It is easy to establish experimentally that electrical parameters change when using a resistor made of different materials. Similar results are obtained by experimenting with different cross sections. With the help of this article you can find out what the resistance of a conductor depends on. The knowledge gained will be useful for creating functional electrical circuits. They are needed for the correct repair and modernization of radio devices, ensuring personal safety during individual work operations.
During the experiment, it is easy to establish the dependence of the measured values on the parameters of the conductor
Concept of electrical resistance of a conductor
The classical definition explains electric current by the movement of “free” (valence) electrons. It is provided by the electric field created by the source. Movement in the metal is hampered not only by the normal components of the crystal lattice, but also by defective areas, impurities, and inhomogeneous areas. During collisions with obstacles, due to the transition of momentum into thermal energy, the temperature increases.
A good example is heating water with a boiler.
In gases, electrolytes and other materials the physics of the phenomenon is somewhat different. Linear relationships are observed in metals and other conductors. The basic relationships are expressed by the well-known formula of Ohm's law:
R (electrical resistance) = U (voltage) / I (current).
For convenience, the inverse quantity, conductivity (G = 1/R), is often used. It denotes the ability of a certain material to pass current with certain losses.
To simplify, the example of a water pipe is sometimes used. A moving fluid is an analogue of a current. Pressure is the equivalent of voltage. By decreasing (increasing) the cross section or position of the locking device, the conditions of movement are determined. In a similar way, the basic parameters of electrical circuits are changed using resistance (R).
For your information. The amount of liquid passing per unit time through the control section of the pipe is the equivalent of electrical power.
Kinds
A conductor is a medium or object that is capable of conducting electric current. Inside it, when connected to an energy source, a charged particle begins to actively move. An ammeter shows the increase in electrical voltage in a circuit. When considering different types of conductors, the electrical conductivity and type of material are taken into account:
- copper;
- aluminum;
- metal;
- gold;
- an alloy of nickel and chromium.
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In the scientific community there is the concept of a superconductor, which is considered ideal. It has a significant dielectric loss angle. When current flows from a circuit, the percentage of bias is taken into account. For a superconductor, this parameter is minimal.
From copper
Copper belongs to the components of group 11 from the table of chemical elements. According to the classification, it is lamellar and is found in different types. Often the substance has a pink tint. In electrical engineering, copper has a low resistivity and shares a niche with silver and gold.
Silver and gold
The material is applicable in the manufacture of wiring and printed circuit boards. Another substance is in demand in the manufacture of electric drives. Considering complex controlled electromechanical systems, it is noticeable that they use windings with low resistivity.
If we evaluate power transformers, they also use this metal, but it is often used with impurities. This is necessary to reduce the electrical conductivity rate. In printed circuit boards, copper is used in tandem with aluminum. When considering radio components, copper-based alloys, which are also characterized by low resistance, remain in demand.
When disassembling personal computers, the substance is found in bronze or brass. Zinc or nickel additives are also used. To increase the elasticity of the conductor, other materials are used, such as tin and zinc. According to the resistivity table, the substance is assigned an indicator of 0.0157 Ohm.
Properties of copper
Made of aluminum
Among the elements of group 13 in the table, aluminum stands out. It is an excellent conductor in a circuit and is made of paramagnetic metal. The color has a silvery tint. The conductor lends itself well to mechanical processing. In addition to significant electrical conductivity, corrosion resistance is noted.
During heat treatment, an oxide film is formed that protects the surface. There are various aluminum compounds found in nature. If we consider standard wire of small cross-section, it is in demand in electric coils. The substance has low density and mass, so analogues are difficult to find. Using aluminum in moving parts can improve their performance.
The conductor is often found in hard drives and audio systems. Wires coated with a layer of varnish remain in demand. There are enameled analogues that are characterized by increased security. Rubber and beryl are used as insulation. Manufacturers produce conductors with a cross section of 0.003 mm.
Properties of aluminum
In addition to inductors, wire can be installed in inductors, loudspeakers, and headphones. Regarding connections, there are options with alunites. Additional information about physical properties:
- low melting point;
- high heat capacity;
- significant hardness;
- weak paramagnetic;
- wide temperature range.
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Aluminum is found in printed circuit boards because it can be stamped. Corrosion resistance is an added benefit. Aluminum conductors are popular and in demand in industry. Resistivity - 0.028 Ohm. It is also necessary to consider the disadvantage of a significant content of impurities.
Made of metal
Among metals, the following are considered common types of conductors:
- lead;
- tin;
- platinum;
- nickel;
- tungsten.
Lead is a group 14 element that can be used as a conductor. It has a maximum density of 11.35 grams per cubic meter. The scope of application is limited because the material is toxic and belongs to heavy metals. The history of the origin of the formula is unclear, there are only guesses.
Metal groups
If we talk about conductor elements, lead nitrate is often used. In power sources and backup units there is a version with chloride. Considering inorganic compounds, the material that stands out is telluride. It is suitable as a thermoelectric conductor and is therefore used in power plants of various capacities. The metal element is also in demand in refrigerators.
If we consider telluride in detail, a significant dielectric constant should be attributed to one of the features. In addition to lead, it contains tin and tellurium. Separately, the substances are found in photoresistors and diodes. If you disassemble semiconductor devices, the elements are contained in stabilizers and indicate the direction of current.
Important! Tin is a conductor from group 14 of chemical elements. The material is safe and does not contain toxic substances.
Along with gold, tin has excellent anti-corrosion properties. Disulfide is often used in technology. Tin dioxide shows the highest resistance value. In batteries it is used in its pure form. When considering galvanic cells, it is worth mentioning manganese-tin dioxide.
Platinum is a conductor from the tenth group of chemical elements. The presented metal has an electrical resistance of 0.098 Ohms and is characterized by increased density. If we consider the scope of application, the substance is often found in laser technology. We are talking about printers, as well as measuring instruments.
Properties of platinum
Additionally, platinum is used in electromagnetic relays. In the presented automatic devices it acts as a conductor. We are talking about mechanical, thermal or optical relays. In electronic sensors, platinum is contained in smaller quantities, but is used due to its wide temperature range. In particular, you can consider an electronic resistance thermometer. The resistive element is mostly made of platinum.
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From gold
The resistivity of gold is 0.023 Ohm. The material belongs to the first group of metals and is soft in physical properties. Gold can also be found in pure form with impurities. The density is 19.32 g/cm³, the scope of application is wide. In industry, the conductor is in demand as solder.
Solder gold
It can be applied to various surfaces and serves as an excellent material for joining workpieces due to its low melting point. Gold is also in demand for protection against corrosion.
Flaws:
- softness of the material;
- subject to pitting corrosion.
If you use a material with additives, the melting point decreases. This also affects the mechanical properties of the substance.
Gold with additives
Dependence on material properties
What does inductance depend on?
For standardization, the unit of measurement was 1 ohm. This resistance creates a column of mercury 1 square meter thick. mm, height – 1063 mm. Measurements are performed while maintaining zero temperature.
To simplify calculations, use the specific resistance value Rsp, which is created by conductors made of other materials (Length x Sectional area = 1,000 mm x 1 sq. mm).
Resistivity (conductivity)
The figure shows Rsp (silver) = 0.016. This means that a meter conductor with a normalized cross-sectional area of 1 mm sq. creates an electrical resistance of 0.016 ohms. Information about other materials can be taken from the reference book.
Effect of temperature
An increase in temperature leads to an increase in vibrations of the metal crystal lattice. Accordingly, electrons encounter more obstacles, which leads to an increase in resistance. The magnitude of the “sensitivity” of the metal resistance to temperature increase is called the temperature coefficient α. The formula for taking into account temperature is as follows: R=Rн*[1+ α*(t°-t°н)], (3) where Rн is the wire resistance under normal conditions (at temperature t°н); t° is the temperature of the conductor. Usually t°n = 20° C. The value of α is also indicated for temperature t°n. Task 4. Calculate the resistance of a copper wire at a temperature t° = 90° C. α copper = 0.0043, Rн = 0.24 Ohm (task 1). Solution: substituting the values into formula (3) we get R = 0.312 Ohm. The resistance of the heated wire being analyzed is 30% greater than its resistance at room temperature.
Dependence on voltage properties
Resistivity
After a simple transformation of the basic formula, you can create the correct expression for voltage:
U = I * R.
The current source generates electricity. The connected resistor consumes energy and is converted into heat. To maintain a certain current strength, it is necessary to set the appropriate voltage.
Measuring circuit, graphs
The graphs show the current-voltage characteristics of different devices. The first two demonstrate linear dependencies in which only the angle of inclination of the straight line changes (depending on the electrical resistance of the resistor).
If you connect a semiconductor diode, the graph will change significantly. From the figure, one can determine the low resistance in the region of positive values of U. However, after a change in polarity, an increase in negative voltage is not accompanied by a similar change in current. One-way conduction is, in particular, used to rectify signals.
In the last graph, the shifted zero current transition point indicates the EMF of the power source. As in the previous example, a small angle relative to the vertical indicates a low internal resistance of the battery.
Physical meaning of reactance
In coils and capacitors, when voltage is applied, energy accumulates in the form of magnetic and electric fields, which takes some time.
Magnetic fields in alternating current networks change following the changing direction of movement of charges, while providing additional resistance.
In addition, a stable phase shift in voltage and current occurs, and this leads to additional losses of electricity.
Geometry Dependency
Conductor inductance
From the section describing the specific parameters it is clear that the electrical resistance of the conductor depends on the length. If we take a silver sample (standardized cross-sectional area 1 sq. mm) with a length of 6.8 m, it is easy to calculate the value R = 6.8 * 0.016 = 0.1088 Ohm.
Other practical problems are solved in a similar way. To create a wire with an electrical resistance of 100 Ohms, you will need a silver wire 6,250 m long = 100/0.016. If we use a metal conductor made of iron, the length will be 833 m = 100/0.12.
The next decisive factor is the cross-sectional area. For clarity, you can use the example of pumping liquid from the main tank into two different containers. It is easy to create the necessary pressure by raising the main tank to a small height. By using tubes with different duct diameters, you can see the difference in the rate of filling of control volumes. If the readings are measured, if desired, it is easy to create proportional dependencies taking into account the initial geometric parameters of the transport channels.
The size of the conductors also matters. Electrical resistance (R) is equal to the specific value for a particular material (Rsp), multiplied by the length (L) and divided by the corresponding cross-section (S). If only the diameter is known, then for a round core you can apply the classic formula from a school geometry course:
S = (π * d2)/4 = (3.14 * d2)/4.
The length is calculated using the converted expression:
L = S * (R/ Rsp).
These proportions demonstrate what resistance depends on.
Ohm's law for a circuit section
Everything that is known about the resistance of conductors, as well as the dependence of current on voltage at the ends of the conductor, is also true for a section of a circuit with any number of conductors. That is, we can formulate Ohm's law for a section of the circuit :
The current strength in the circuit is directly proportional to the voltage at the ends of this section and inversely proportional to the electrical resistance of this section of the circuit:
,
where R is the resistance of the circuit section, which depends only on the properties of the conductors that make up the section.
Ohm's law is one of the most important physical laws; most of the calculations of electrical circuits in electrical engineering are based on this law.
Calculation of conductor resistance
Simplified methods that need to be adjusted taking into account real conditions were discussed above. Thus, temperature has a significant effect on the conductivity of materials. In serial conductors (copper, aluminum), the value of this parameter increases in the proportion of 0.3-0.5% for each degree. In carbon-based compositions and electrolytes, the opposite effect is observed - a decrease in resistance.
Without holding strings or other devices for tricks, real levitation using superconductivity is provided
The experiment shown in the figure can be reproduced by lowering the temperature of the metal to “absolute zero” (-273°C). With such extreme cooling, the atomic lattice is fixed in a stable position.
This state creates ideal conditions for the movement of electrons. The absence of obstacles is accompanied by minimal losses, which explains the promising direction for creating efficient energy transmission lines. The example in the figure demonstrates improved operational parameters of transport communications. In this case, friction forces can be eliminated.
Combination of airless tube and superconductivity improves performance of advanced transport systems
It is clear that to improve economic performance it is necessary to increase the operating temperature while maintaining good conductivity. However, the latest scientific achievements in the relevant field allow us to count on positive results in the near future.
It should be emphasized! In practice, different computing technologies may be needed. For example, the material is unknown. It is difficult to identify it by external signs. For high-quality chemical laboratory analysis, in addition to the appropriate skills, special equipment is required.
However, if necessary, it is easy to derive the specific indicator:
Rsp = R * S / L.
Geometric parameters are measured with standard tools (ruler, caliper). According to a typical measurement scheme, electrical resistance is determined using a multimeter. To calculate Rsp, use the formula presented above. In the directory, select the position corresponding to the calculation result. Using the same technique, you can determine other unknown values, for example, the length of the cable in an underground route.
In actual calculations, the reactive components of the conductors are taken into account to improve accuracy. For example, the inductance of a long straight line is determined by the formula:
AND = (m0/2π) * L *(mc * ln(L/r) +1/4m,
Where:
- m – magnetic permeability of the material (o – constant, c – environment);
- r and L are the radius and length of the conductor, respectively.
As the frequency increases, it is necessary to take into account current spreading in the surface zone and vortex changes.
The theoretical knowledge presented will be useful for calculating and creating a rheostat - a device with adjustable resistance. They are needed to prevent electrical injuries using precise calculations of protective circuits and specialized circuit breakers (fuses).
How to calculate wire resistance - tips for novice electricians
Good day! I'm planning to connect an electric hob and oven at home myself. Due to the fact that I heard that standard wiring may not withstand such a voltage and will begin to overheat, I decided to run separate wires from the panel through an additional circuit breaker.
I already have the machine, but I don’t know how to select the wire cross-section. Tell me how to calculate the resistance of the wires to suit my needs - I will have to throw 20 meters of wire, no less.
The unit of electrical resistance was named after this man.
Reply to reader
Greetings, unfortunately unintroduced reader! Naturally, we will help you with the calculations, but we still recommend that you involve a specialist in the problem, because you will need to choose the right not only the conductor, but also the machine. However, if you know for sure that the parameters of the machine are suitable, then you have nothing left...
Theory and practice
So, if a person is even a little familiar with the basics of electrical engineering, he should know that the thicker the wire, the lower the resistance.
- Theoretically, this can be compared to a water pipe through which water flows. If the diameter of the pipe is sufficient, then the liquid flows through it without experiencing any hydraulic resistance, and vice versa, a small hole increases the pressure in the pipe, the throughput drops, and the hydraulic resistance increases.
- Also, the flow of electrons can be represented as water trying to flow inside the wire. However, electricity is a completely different nature, and accordingly its physical properties are different.
- What can cause too high resistance? The most common thing is a voltage drop, as a result of which some incandescent lamp will burn dimmer, and some electrical appliance will not be able to start.
- A direct consequence of the passage of a powerful current through a conductor with a sufficiently high resistance will be its overheating.
From the author! One day we connected the welding machine to, well, a very bad extension cord, and after a few minutes of work the wire literally caught fire. Fortunately, a short circuit did not occur, but it was very likely. As is clear, such situations are unacceptable in a residential area.
We recommend proceeding in the following sequence:
- First of all, find out exactly how much load both of your devices create when operating at maximum power. We are interested in current strength, measured in Amperes, or power - Watts.
- You can easily find these parameters in the product data sheets.
- If both devices are powered from the same line, then sum the resulting values.
- Next, use the table, which will allow you to accurately determine the wire cross-section.
The photo shows a table for selecting conductor cross-sections
- As can be seen from the table above, the maximum current for a copper wire with an area of 0.5 should not exceed 11 Amperes.
Advice! Today the use of aluminum wires is not allowed in residential premises. Only copper ones are used.
- In principle, one could limit ourselves to these data, adding some margin, but such tables do not show what the maximum resistance of the wire should be, that is, the length of the conductor is not taken into account. Therefore, for greater accuracy, calculations are indispensable.
Calculating resistance
All data can be obtained from the tables.
So, we remember - the wire is thicker, the resistance is less. The following will provide instructions on how to calculate everything accurately.
- To do this, we need to find out the resistivity of the conductor material. In ordinary networks you are unlikely to find silver wires, so we take standard copper as a basis. It is 0.017.
- The wire resistance itself is calculated using the following formula: ; where R is the resistance, p is the resistivity of the conductor, l is the length of the wire and s is its cross-sectional area.
- Let's assume that your stoves together can load a network of 16 Amps, this means that we can take a wire with an area of 0.75 mm2. We remember that you require a minimum of 20 meters. So, we consider: 0.017*20/0.75 = 0.45 Ohm
- You can use the table, but the result will not be as accurate. We see that 100 meters of copper wire of the cross-section we need has a resistance of 2.38 Ohms. We divide this value by five (up to 20 meters) and get 0.476 Ohms - the difference is at the level of error, but still.
- Due to the fact that electricity flows through two wires, we multiply the resulting value by 2 and get 0.9 Ohm.
- Now you can calculate the voltage loss using the formula: dU = R*I = 0.9*16 = 14.4 Volts.
- We convert the resulting voltage into a percentage: 14.4V/220V*100 = 6.54%
According to existing standards, 5% voltage loss is allowed. As you can see, in our case the value turned out to be larger, which means that the conductor resistance is too high, so we increase the cross-section of the wire and repeat the calculations.
So, we have found the resistance of the wire, and as you can see, doing this with your own hands and head is not so difficult. The attached video will help you understand the material further. Approach the matter wisely, because the price is the safety of you and your home.
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