In practice, the problem of findingresistance of conductors and resistors at various ways of connection. The article considers how the resistance is calculated for parallel connection of conductors and some other technical issues.
All conductors have the property of impeding the flow of electric current, it is usually called the electrical resistance R, it is measured in ohms. This is the main property of conductor materials.
For conducting electrical calculations, the resistivity is applied - ρ Ohm · m / mm2. All metals are good conductors, mostCopper and aluminum were used, iron is much less commonly used. The best conductor is silver, it is used in the electrical and electronic industries. Alloys with a high resistance value are widespread.
When calculating the resistance, a formula known from the school physics course is used:
R = ρ · l / S, S - sectional area; l is the length.
If you take two conductors, then their resistance when connected in parallel will become less due to the increase in the total cross section.
For practical calculations of the operating modes of conductors, the concept of current density is used - δ A / mm2it is calculated by the formula:
δ = I / S, I is the current, S is the cross section.
The current passing through the conductor heats it.The greater the δ, the stronger the conductor heats up. For wires and cables, the norms of permissible density are developed, which are given in the Rules for Electrical Installations (Electrical Installation Rules). For conductors of heating devices have their own current density standards.
If the density δ is higher than acceptable, the conductor may be destroyed, for example, if the cable overheats, the insulation is destroyed.
The rules govern the calculation of conductors for heating.
Any conductor is much more convenient to depict oncircuits as electrical resistance R, then they are easy to read and analyze. There are only three ways to connect resistances. The first method is the easiest - serial connection.
The photo shows that the impedance is: R = R1 + R2 + R3.
The second method is more complicated - parallelcompound. Calculation of resistance with parallel connection is performed in stages. Calculate the total conductivity G = 1 / R, and then the impedance R = 1 / G.
You can do differently, first calculate the total resistance with parallel connection of resistors R1 and R2, then repeat the operation and find R.
The third method of connection is the most difficult - a mixed compound, that is, all the considered options are present. The scheme is shown in the photo.
To calculate this circuit, it should be simplified; for this purpose, resistors R2 and R3 are replaced with one R2.3. It turns out a simple scheme.
Now it is possible to calculate the resistance in parallel connection, the formula of which has the form:
R2,3,4 = R2,3 · R4 / (R2,3 + R4).
The circuit becomes even simpler, there remain a series-connected resistors. In more complex situations, the same conversion method is used.
In electronic engineering, in the production of printedboards, conductors represent a thin strip of copper foil. Due to the small length of the resistance they have little, they can be neglected in many cases. For these conductors, resistance when parallel connected decreases due to the increase in cross-section.
A large section of conductors representwinding wires. They are available in different diameters - from 0.02 to 5.6 millimeters. For high-power transformers and electric motors, copper trunks of rectangular section are produced. Sometimes, when repairing, they replace the wire of large diameter with several parallel ones of a smaller size.
A special section of conductors are wires andcables, the industry provides the widest choice of brands for a wide variety of needs. It is often necessary to replace one cable with several smaller sections. The reasons for this are very different, for example, a cable with a section of 240 mm2 It is very difficult to lay on the highway with steep bends. It is replaced by 2 × 120 mm2, and the problem is solved.
The conductor is heated by the current flowing, if itsthe temperature exceeds the permissible, destruction of the insulation occurs. PUE provides for the calculation of the conductors for heating, the initial data for it are the current strength and the conditions of the external environment in which the conductor is laid. According to these data, the recommended conductor cross-section (wire or cable) is selected from the tables in the ПУЭ.
In practice, there are situations where the loadon the active cable has greatly increased. There are two exits - to replace the cable with another one, it can be expensive, or lay one more parallel to it in order to unload the main cable. In this case, the resistance of the conductor with a parallel connection decreases, hence the heat release decreases.
To choose the right cross-section of the second cable,use the OLC tables, it is important not to make a mistake with the definition of its operating current. In this situation, the cooling of the cables will be even better than that of one. It is recommended to calculate the resistance when two cables are connected in parallel in order to more accurately determine their heat dissipation.
With the location of the consumer RMr. at a large distance L from the energy source U1 there is quite a large voltage drop on the wires of the line. To consumer RMr. voltage U arrives2 well below the initial u1. In practice, various electrical equipment, which is connected to the line in parallel, acts as a load.
To solve the problem, calculate the resistance when all equipment is connected in parallel, so is the load resistance RMr.. Next, determine the resistance of the wires of the line.
Rl = ρ · 2L / S,
Here S is the wire section, mm2.
Next, the line current is determined: I = U1/ (Rl + RMr.). Now, knowing the current, determine the voltage drop on the wires of the line: U = I · Rl. It is more convenient to find it as a percentage of U1.
U% = (I · Rl/ U1) · 100%
The recommended value of U% is no more than 15%. The above calculations are applicable for any kind of current.
