All electronic devices contain resistors, which are their main element. With it, the current in the electric circuit is changed. The article describes the properties of resistors and methods for calculating their power.
The purpose of the resistor
To adjust the current in electrical circuits, resistors are used. 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 lower 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 widely used in electrical devices.
In this scheme, the current from the source is divided into two, inversely proportional to the resistances of the resistors.
In addition to adjusting the current, resistors are used in voltage dividers. In this case, Ohm's law is again used, but in a slightly different form:
U = I ∙ R (2)
From formula (2) it follows that with increasing resistance, the voltage increases. This property is used to build voltage divider circuits.
It is clear from the circuit and formula (2) that the voltages across the resistors are distributed in proportion to the resistances.
The image of resistors in the circuits
According to the standard, resistors are represented by a rectangle with dimensions of 10 x 4 mm and are indicated by the letter R. Often the power of resistors is 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 repair and analysis of the circuit, power of resistors is often given , the designation of which is performed according to GOST 2.728-74.
Device Specifications
The main characteristic of the resistor is the nominal resistance R n , which is indicated on the circuit near the resistor and on its housing. 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 producing resistors, all of which have both advantages and disadvantages. In principle, there is no technology that would make it possible to accurately manufacture a resistor with a given resistance value.
The second important characteristic is the deviation of the resistance. It is measured in% of the nominal R. There is a standard series of resistance deviations: ± 20, ± 10, ± 5, ± 2, ± 1%, and then up to the value of ± 0.001%.
The next important characteristic is the power of the resistors. During operation, they are heated by the current flowing through them. If the dissipated power exceeds the permissible value, the device will fail.
Resistors change their resistance when heated, so for devices operating in a wide temperature range, another characteristic is introduced - the temperature coefficient of resistance. It is measured in ppm / ° C, i.e. 10 -6 R n / ° C (ppm of R n at 1 ° C).
Series resistors
Resistors can be connected in three different ways: serial, parallel, and mixed. With a series connection, the current alternately passes through all the resistances.
With this connection, the current at any point in the circuit is the same, it can be determined according to 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 Ohms;
I = U / R = 100/390 = 0.256 A.
Now you can determine the power in the series connection of resistors, it is calculated by the formula:
P = I 2 ∙ R = 0.256 2 ∙ 390 = 25.55 W.
Similarly, the power of the remaining resistors is determined:
P 1 = I 2 ∙ R 1 = 0.256 2 ∙ 200 = 13.11 W;
P 2 = I 2 ∙ R 2 = 0.256 2 ∙ 100 = 6.55 W;
P 3 = I 2 ∙ R 3 = 0.256 2 ∙ 51 = 3.34 W;
P 4 = I 2 ∙ R 4 = 0.256 2 ∙ 39 = 2.55 W.
If you add the power of the resistors, you get the full P:
P = 13.11 + 6.55 + 3.34 + 2.55 = 25.55 watts.
Parallel connection of resistors
With a parallel connection, all the beginning of the resistors are connected to one node of the circuit, and the ends to the other. With this connection, the current branches and flows through each device. The current value, 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 according to the well-known formula:
1 / R = 1 / R 1 + 1 / R 2 + 1 / R 3 + 1 / R 4 = 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 ohms.
Using Ohm's law, they 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 the parallel-connected resistors according to the formula:
P = I 2 ∙ R = 6.024 2 ∙ 16.6 = 602.3 W.
According to Ohm's law, the current through the resistors is calculated:
I 1 = U / R 1 = 100/200 = 0.5 A;
I 2 = U / R 2 = 100/100 = 1 A;
I 3 = U / R 1 = 100/51 = 1.96 A;
I 1 = U / R 1 = 100/39 = 2.56 A.
Using a slightly different formula, you can calculate the power of resistors in parallel connection:
P 1 = U 2 / R 1 = 100 2/200 = 50 W;
P 2 = U 2 / R 2 = 100 2/100 = 100 W;
P 3 = U 2 / R 3 = 100 2/51 = 195.9 W;
P 4 = U 2 / R 4 = 100 2/39 = 256.4 watts.
If all this is added up, then the power of all resistors will turn out:
P = P 1 + P 2 + P 3 + P 4 = 50 + 100 + 195.9 + 256.4 = 602.3 W.
Mixed compound
Mixed resistor circuits contain a series and simultaneously parallel connection. This circuit is easy to convert by replacing the parallel connection of resistors with a series. To do this, first replace the resistances R 2 and R 6 with their total R 2,6 , using the formula below:
R 2.6 = R 2 ∙ R 6 / R 2 + R 6.
In the same way, two parallel resistors R 4 , R 5 are replaced by one R 4,5:
R 4,5 = R 4 ∙ R 5 / R 4 + R 5 .
The result is a new, simpler scheme. Both schemes are shown below.
The power of resistors in a mixed-connection circuit is determined by the formula:
P = U ∙ I.
To calculate by this formula, first find the voltage at each resistance and the amount of current through it. You can use another method to determine the power of resistors. For this, the formula is used:
P = U ∙ I = (I ∙ R) ∙ I = I 2 ∙ R.
If only the voltage across the resistors is known, then another formula is used:
P = U ∙ I = U ∙ (U / R) = U 2 / R.
All three formulas are often used in practice.
Calculation of circuit parameters
Calculation of the circuit parameters consists in finding unknown currents and voltages of all branches in sections of the electric circuit. Having this data, you can calculate the power of each resistor included in the circuit. Simple calculation methods were shown above, but in practice the situation is more complicated.
In real circuits, the connection of resistors with a star and a triangle 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 incorporates 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 to node 3, and R3-0 and R1-0 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, according to Ohm's law, the current through the source is found. Using this law, it is easy to find currents in all branches.
How to determine the power of resistors after finding all the currents? To do this, use the well-known formula: P = I 2 ∙ R, applying it for each resistance, we find their power.
Experimental determination of the characteristics of circuit elements
To experimentally determine the necessary characteristics of the elements, it is necessary to assemble a given circuit from real components. After that, with the help of electrical measuring instruments carry out all the necessary measurements. This method is time consuming and expensive. The developers of electrical and electronic devices use simulation programs for this purpose. With the help of them, all the necessary calculations are performed, and the behavior of the circuit elements in various situations is modeled. Only after that a prototype of a technical device is assembled. One such common program is National Instruments' powerful Multisim 14.0 modeling 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. Multiplying the measurement results, we obtain the desired power.
From this circuit we determine the resistance power R3:
P 3 = U ∙ I = 1,032 ∙ 0.02 = 0.02064 W = 20.6 mW.
The second method is direct power measurement using a wattmeter.
From this diagram it can be seen that the resistance power R3 is P 3 = 20.8 mW. The discrepancy due to the error in the first method is greater. In the same way, the powers of the remaining elements are determined.