All electronic devices contain resistors as their main element. It is used to change the amount of current in an electrical circuit. The article presents the properties of resistors and methods for calculating their power.
Resistor Assignment
Resistors are used to regulate the current in electrical circuits. This property is defined by Ohm's Law:
I=U/R (1)
From formula (1) it is clearly seen that the lower the resistance, the stronger the current increases, and vice versa, the smaller the value of R, the greater the current. It is this property of electrical resistance that is used in electrical engineering. Based on this formula, current divider circuits are created, which are widely used in electrical devices.
In this circuit, the current from the source is divided into two, inversely proportional to the resistances of the resistors.
Besides current regulation, resistors are used in voltage dividers. In this case, Ohm's law is used again, but in a slightly different form:
U=I∙R (2)
From formula (2) it follows that as the resistance increases, the voltage increases. This propertyused to build voltage divider circuits.
From the diagram and formula (2) it is clear that the voltages across the resistors are distributed in proportion to the resistances.
Image of resistors on diagrams
According to the standard, resistors are depicted as a rectangle with dimensions of 10 x 4 mm and are denoted by the letter R. The power of resistors is often indicated on the diagram. The image of this indicator is performed by oblique or straight lines. If the power is more than 2 watts, then the designation is made in Roman numerals. This is usually done for wirewound resistors. Some states, such as the United States, use other conventions. To facilitate the repair and analysis of the circuit, the power of resistors is often given, the designation of which is carried out in accordance with GOST 2.728-74.
Device Specifications
The main characteristic of the resistor is the nominal resistance Rn, which is indicated on the diagram near the resistor and on its case. The unit of resistance is ohm, kiloohm and megaohm. Resistors are made with resistance from fractions of an ohm to hundreds of megaohms. There are many technologies for the production of resistors, all of them have both advantages and disadvantages. In principle, there is no technology that would allow absolutely precise manufacturing of a resistor with a given resistance value.
The second important characteristic is the resistance deviation. It is measured in % of nominal R. There is a standard range of resistance deviation: ±20, ±10, ±5, ±2, ±1% and further up tovalues ±0.001%.
The next important characteristic is the power of the resistors. During operation, they heat up from the current passing through them. If the power dissipation exceeds the allowable value, the device will fail.
Resistors change their resistance when heated, so for devices operating in a wide temperature range, one more characteristic is introduced - the temperature coefficient of resistance. It is measured in ppm/°C, i.e. 10-6 Rn/°C (millionth of Rnby 1°C).
Series connection of resistors
Resistors can be connected in three different ways: series, parallel and mixed. When connected in series, the current passes through all the resistances in turn.
With such a connection, the current at any point in the circuit is the same, it can be determined by Ohm's law. The total resistance of the circuit in this case is equal to the sum of the resistances:
R=200+100+51+39=390 Ohm;
I=U/R=100/390=0, 256 A.
Now you can determine the power when resistors are connected in series, it is calculated by the formula:
P=I2∙R=0, 2562∙390=25, 55 W.
The power of the remaining resistors is determined in the same way:
P1=I2∙R1=0, 256 2∙200=13, 11 Tue;
P2=I2∙R2=0, 256 2∙100=6.55W;
P3=I2∙R3=0, 256 2∙51=3, 34W;
P4=I2∙R4=0, 256 2∙39=2, 55 Tues.
If you add the power of the resistors, you get the full P:
P=13, 11+6, 55+3, 34+2, 55=25, 55 Tues.
Parallel connection of resistors
In a parallel connection, all the beginnings of the resistors are connected to one node of the circuit, and the ends to another. With this connection, the current branches and flows through each device. The magnitude of the current, according to Ohm's law, is inversely proportional to the resistances, and the voltage across all resistors is the same.
Before you find the current, you need to calculate the total conductivity of all resistors using the well-known formula:
1/R=1/R1+1/R2+1/R3 +1/R4=1/200+1/100+1/51+1/39=0, 005+0, 01+0, 0196+0, 0256=0, 06024 1/Ohm.
Resistance is the reciprocal of conductivity:
R=1/0, 06024=16.6 ohm.
Using Ohm's law, find the current through the source:
I=U/R=100∙0, 06024=6, 024 A.
Knowing the current through the source, find the power of resistors connected in parallel by the formula:
P=I2∙R=6, 0242∙16, 6=602, 3 Tues.
According to Ohm's law, the current through resistors is calculated:
I1=U/R1=100/200=0.5A;
I2=U/R2=100/100=1 A;
I3=U/R1=100/51=1, 96A;
I1=U/R1=100/39=2, 56 A.
A slightly different formula can be used to calculate the power of resistors in parallel connection:
P1=U2/R1=100 2/200=50W;
P2=U2/R2=100 2/100=100W;
P3=U2/R3=100 2/51=195.9W;
P4=U2/R4=100 2/39=256, 4 Tues.
If you add it all up, you get the power of all the resistors:
P=P1+ P2+ P3+ P 4=50+100+195, 9+256, 4=602, 3 Tues.
Mixed connection
Schemes with mixed connection of resistors contain serial and parallel connection at the same time. This circuit is easy to convert by replacing the parallel connection of resistors with series ones. To do this, first replace the resistances R2 and R6 with their total R2, 6, using the formula below:
R2, 6=R2∙R6/R 2+R6.
In the same way, two parallel resistors R4, R5 are replaced by one R4, 5:
R4, 5=R4∙R5/R 4+R5.
The result is a new, simpler circuit. Both schemes are shown below.
The power of resistors in a mixed connection circuit is determined by the formula:
P=U∙I.
To calculate this formula, first find the voltage across each resistance and the amount of current through it. You can use another method to determine the power of the resistors. For thisthe formula is used:
P=U∙I=(I∙R)∙I=I2∙R.
If only the voltage across the resistors is known, then another formula is used:
P=U∙I=U∙(U/R)=U2/R.
All three formulas are often used in practice.
Calculation of circuit parameters
Calculation of circuit parameters is to find unknown currents and voltages of all branches in the sections of the electrical circuit. With this data, you can calculate the power of each resistor included in the circuit. Simple calculation methods have been shown above, but in practice the situation is more complicated.
In real circuits, the connection of resistors with a star and a delta is often found, which creates significant difficulties in the calculations. To simplify such schemes, methods have been developed for converting a star into a triangle, and vice versa. This method is illustrated in the diagram below:
The first circuit has a star connected to nodes 0-1-3. Resistor R1 is connected to node 1, R3 to node 3, and R5 to node 0. In the second diagram, triangle resistors are connected to nodes 1-3-0. Resistors R1-0 and R1-3 are connected to node 1, R1-3 and R3-0 are connected to node 3, and R3-0 and R1-0 are connected to node 0. These two schemes are completely equivalent.
To go from the first circuit to the second, the resistances of the triangle resistors are calculated:
R1-0=R1+R5+R1∙R5/R3;
R1-3=R1+R3+R1∙R3/R5;
R3-0=R3+R5+R3∙R5/R1.
Further transformations are reduced to the calculation of parallel and series-connected resistances. When the impedance of the circuit is found, the current through the source is found according to Ohm's law. Using this law, it is not difficult to find the currents in all branches.
How to determine the power of the resistors after finding all the currents? To do this, use the well-known formula: P=I2∙R, applying it for each resistance, we will find their power.
Experimental determination of the characteristics of circuit elements
To experimentally determine the desired characteristics of elements, it is required to assemble a given circuit from real components. After that, with the help of electrical measuring instruments, all necessary measurements are performed. This method is labor intensive and expensive. Designers of electrical and electronic devices use simulation programs for this purpose. With the help of them, all the necessary calculations are made, and the behavior of the circuit elements in various situations is modeled. Only after that is a prototype of a technical device assembled. One such common program is National Instruments' powerful Multisim 14.0 simulation system.
How to determine the power of resistors using this program? This can be done in two ways. The first method is to measure current and voltage with an ammeter and voltmeter. By multiplying the measurement results, the required power is obtained.
From this circuit we determine the resistance power R3:
P3=U∙I=1, 032∙0, 02=0, 02064 W=20.6mW.
The second method is the direct measurement of power atusing a wattmeter.
From this diagram it can be seen that the power of the resistance R3 is P3=20.8 mW. The discrepancy due to the error in the first method is greater. The powers of other elements are determined in the same way.
