Various types of connections of standard passive elements are used to solve practical problems in electrical and radio engineering. Using certain circuit configurations, they change the voltage and currents in circuits and create protective and control devices. Below is a parallel connection of resistors. In addition to comparison with other options, manual and automated calculation technologies are considered with recommendations for applying knowledge in practice.
Different types of resistor connections
Differences from serial and mixed connections
Parallel connection of resistors
Other connection methods are clear from the examples shown in the picture. Without special calculations, it is clear that parallel connection of resistors creates several current paths. Consequently, in individual circuits its strength will be less compared to the control points at the input and output. However, the voltage in the marked places remains unchanged.
Connecting resistors in series increases the overall electrical resistance. The current in this circuit (based on basic principles) will not change. However, at each passive element the corresponding voltage drop can be detected by the measuring instrument.
A mixed version is a combination of the compounds presented above. Various combinations are used to divide voltage and solve other problems. To simplify calculations, we summarize the sequence of connected resistances in individual circuits:
Rtot = R1 + R2 + … + Rn.
Regardless of the complexity of the circuit, the currents at the input and output will be the same according to Kirchhoff’s first law.
Atomizers for winding
Before purchasing an atomizer, it is better to seek advice from specialists, namely experienced vapers.
The most popular models among the vaping community are as follows:
- Kanger SubTank is a popular and highly advertised self-propelled clearomizer that has won many followers for its ability to use both factory and homemade coils. Recently a modification of this model was released - TopTank. The new version allows you to refill the electronic cigarette from above, thus without unscrewing the device from the mod.
- Kayfun is a Russian-made clear, which is created only for self-winding;
- Billow v2 – the main difference of this clearomizer is the ability to install two coils, and not, as usual, one.
- Zefirus is a double-coil clear of excellent quality, which is also loved by vapers for its ability to work with both homemade heads and factory ones.
- Velocity – unlike previous models, it is a drip device, not a clearomizer. That is, its device does not have a liquid tank. The refill must be dripped onto the spiral. Although not very convenient to use, Velocity will provide you with excellent taste and a lot of thick vapor.
Calculation of parallel connection of resistors
Series and parallel connection of batteries
For a better understanding of the processes, you should consider in detail the diagram below. Measuring instruments are conventionally shown at control points (circuit breaks). Similarly, connect a multimeter to clarify the results of theoretical calculations. To keep the explanation simple, an “ideal” DC source is used. Its resistance is not taken into account in the calculations. Similarly, capacitive (inductive) reactive components, which can create minor nonlinear distortions, are ignored.
Electrical diagram with explanatory formulas
In the example under consideration, the current (I) flows in a closed loop from the positive to the negative electrode of the battery. At the input of the parallel section (point “a”) it is divided into I1 (I2), passing through different branches with electrical resistances R1 (R2), respectively. At point “b” the currents are combined.
If you connect the multimeter terminals to the positive terminal of the battery and the input point, and then repeat the measurement at the output, the same values will be determined. However, in individual branches the currents will differ if different resistances are used (R1≠R2). Adding the readings will confirm the equality of the sum to the previously obtained measurement results at the input (output). Interim conclusion, confirmed experimentally:
Itotal = I1 + I2.
Next, you can check the potential difference at the power supply terminals (Uip), at the test points (Uab) and on individual resistors (UR1 and UR2). It is easy to verify that Uip = Uab = UR1 = UR2. For individual branches the following proportions will apply:
- UR1 = I1 * R1;
- UR2 = I2 * R2.
However, taking into account the measurement results, we can equate both sides of the expressions:
UR1 = UR2 = I1 * R1 = I2 * R2.
A simple transformation yields the following relation:
I1/I2 = R2/R1.
Based on this formula, the following important conclusion must be made: currents are inversely proportional to the electrical resistance in the corresponding branches of the parallel circuit.
Example with source data:
- battery Uip = 6V;
- resistance of parallel resistors: R1 = 50 Ohm, R2 = 150 Ohm.
Calculation:
- you can find the current in the first branch using the formula: I1 = Uip / R1 = 6/50 = 0.12A = 120 mA;
- calculate in the same way: I2 = Uip / R2 = 6/150 = 0.04A = 40 mA;
- total value: Itotal = I1 + I2 = 120 + 40 = 160 mA;
- the principle of proportionality noted above is observed: I1/I2 = R2/R1 = 50/150 = 40/120 ≈ 0.333.
It should be noted that the current strength is different in individual branches. For clarity, we can recall an example with an analogue from water pipes. In a branched section, more liquid will pass through a duct with a large diameter compared to the other section during a control time interval. Electrical resistance works in a similar way. When increasing the rating of a passive element, additional obstacles to the passage of current are created.
To calculate complex circuits, equivalent resistance technology is used. This term denotes the calculated value (Req), which is equal to the sum of the measured parameters of the individual components in a certain section of the circuit. The easiest way to do the calculations is to connect resistors (values from the example) in series:
Req = R1 + R2 = 50 + 150 = 200 Ohm.
The option with a parallel circuit is discussed in detail below:
- according to Ohm's law, the following expression is valid for the entire chain: Itot = Uip/ Req;
- in separate branches: I1 = U1/ R1 (I2 = U2/ R2);
- according to Kirchhoff's law for each wire: I = I1+ I2;
- transformation of the listed relations allows us to draw an intermediate conclusion: Uip/ Req = U1/ R1 + U2/ R2;
- taking into account the equality of voltages: Uip = U1 = U2, you can redo the previous formula as follows: Uip/ Req = Uip / R1 + Uip / R2 = Uip (1/R1 + 1/R2);
- by dividing by the common factor Uip, the final expression is obtained: 1/Req = 1/R1 + 1/R2.
The last position allows us to draw several important conclusions:
- total conductivity (the reciprocal of electrical resistance) is equal to the sum of the conductivities of parallel sections of the circuit;
- the equivalent resistance can be calculated by dividing one by the conductivity;
- Req in a parallel connection is always less than the smallest passive component in the circuit.
Winding materials
To make a working atomizer, you need cotton wool and wire. Cotton wool is used as a wick, and a coil for an electronic cigarette is wound from wire. During the vaping process, the wick is wetted with liquid, then steam is produced under the influence of the heated coil and incoming air at the moment of inhaling.
Materials for the spiral
So, let's look at the commonly used materials for winding coils for electronic cigarettes:
- Nichrome - primarily attracts with its low price, as well as ease of creating windings;
- Fechral is an analogue of nichrome, but it does not contain nickel. The cost is even lower than that of nichrome, the service life and quality when used are also lower;
- Stainless steel is one of the cheapest and most accessible materials that has a long service life. Despite its advantages, it is used infrequently, since the material is not convenient for winding;
- Nickel - in addition to its high price, it also has high quality, so it is not recommended for beginners for “experience”;
- Titanium is not inferior in properties to nickel. As an advantage, it does not emit harmful substances when overheated, which other analogues cannot boast of. Despite this, experts say that the release of harmful substances begins when the device overheats at 600 °C, while mods do not heat up more than 350 °C.
Wick materials
There are not many options for making a wick. Let's take a closer look:
- Silica cord is rarely used today due to noticeable disadvantages: it gets dirty quickly, produces little steam and taste, and does not conduct liquid well enough;
- Cotton wool – we are not talking about medical cotton wool, which is sold in all pharmacies. You need it uncleaned and unsterile. Otherwise, instead of the taste of raspberries, you will enjoy the taste of medicines. Even cotton pads can become an analogue. A significant advantage is accessibility and low cost;
- Japanese cotton is easy to use and does not create an aftertaste. Relatively inexpensive material, but for “beginners” it may seem expensive. You can purchase it in online stores or stores specializing in vaping in the city.
How to calculate complex resistor wiring diagrams
If you combine a larger number of elements, you need to add the required number of terms to the formulas considered.
Initial data:
- DC source 12V;
- resistance of parallel resistors, Ohm: 10, 40, 60, 80.
Calculation:
- basic formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4;
- Substituting the original data, calculate the conductivity: G = 1/Req = 1/10 + 1/40 + 1/60 +1/80 = 0.1 + 0.025 + 0.0166 +0.0125 = 0.1541;
- equivalent resistance: Req = 1/0.1541 ≈ 6.5 Ohm;
- current in the circuit: Itot = Uip/ Req = 12/ 6.5 ≈ 1.85 A.
Complex circuits
Using a similar technology, calculations are made for more complex circuits. The figure shows the resistance values. In both cases, the same power source is used with Uip = 12V.
Calculation 1 (serial and parallel connection):
- for each parallel section you can use the formula: Rtot = 1/ (1/R1 + 1/R2) = R1*R2/R1 + R2;
- equivalent resistance of the first part: Req1 = (2*4)/ (2+4) = 1.3 Ohm;
- second: Req2 = (15*5)/ (15+5) = 3.75 Ohm;
- general: Req = 1.3 + 10 + 3.75 = 15.05 Ohm;
- Itot = Uip/ Req = 12/ 15.05 ≈ 0.8 A.
Calculation 2 (complex parallel connection):
- in this option, first calculate the conductivity of the part (R3, R4, R5) using the formula: G345 = 1/5 + 1/10 + 1/20 = 7/20 = 0.35 sim;
- Req (345) = 1/0.35 ≈ 2.857 Ohm;
- total value for the circuit: R1 + R2 = 20 Ohm;
- By analogy with the previous method, they determine: G12345 = 0.4 sim and Req(12345) = (20*2.857)/ 20 + 2.857) ≈ 2.5 Ohm;
- after adding the last element (R6 = 7.5 Ohm), the final result is obtained: Req = 2.5 + 7.5 = 10 Ohm;
- division determines the current strength in the load connected to a 12 V current source: I = 12/10 = 1.2 A.
The last example uses an additional circuit component (R6). Accordingly, for this circuit the above-discussed proportion of equal voltages (source and connected load) will not be satisfied.
In this case, the potential difference across the sixth resistor will be:
U6 = I *R6 = 1.2 * 7.5 = 9 V.
Accordingly, the voltage between the control points will change:
Uab = I * Reeq(12345) = 1.2*2.5 = 12-9 =3V.
The second part of the formula demonstrates a test by subtracting voltages (Uip - U6).
Types of winding
There are five types of coils. Many vapers are probably already familiar with them, but for beginners it will be useful to know what types of electronic cigarette coils there are.
- Microcoil is a small spiral, where the turns are located very close to each other. Due to its size, the coil is ideal for small clearomizers, while the heating area is large, which provides a lot of steam. When creating a microcoil, be careful not to cause a short circuit.
- Space coil is a standard coil in which the coils are separated by a small space (hence the name). This technology allows the cotton wool not to burn, but the liquid to be evenly saturated throughout the entire wick. Despite the convenient winding, the space coil will not give you much steam.
- “Pigtail” - a spiral is wound from two intertwined wires, which visually resemble a pigtail. Due to the increased heating area, the amount of steam and the quality of taste increases. However, there is one drawback - there is a possibility of “pulling out” not the vapor, but the smoking liquid.
- “Parallel” is an analogue of the previous type of winding, only two wires in a spiral run parallel, and are not intertwined into a pigtail. Guarantees a large amount of steam. When replacing the coil in an electronic cigarette, the main difficulty is securing the ends of the two parallel wires.
- Art coils - the main feature of this type of winding is the patterned weaving, which is more of an art than a way to wind a spiral. Only “gurus” in their field know the technique of art coils. The large heating area gives an amazing effect in the form of a huge amount of steam and a pronounced taste of the liquid.
Current in a circuit of parallel connected resistors
When considering the corresponding sections of branched circuits, it is necessary to remember that the currents at the input and output of each node are equal, as well as before and after the group of parallel resistors. This rule will help check the correctness of the calculations. If the marked correspondence is not met, the calculation error is eliminated.
Current strength in parallel connection
Using the initial data discussed above for two complex circuits, a calculation can be made for each individual branch.
Example 1:
- the total current in the circuit is 0.8 A;
- the distribution of voltages in individual sections is easy to determine from the calculated equivalent resistances: U12 = I * Req1 = 0.8 * (2*4)/ (2+4) = 0.8 * 1.3 = 1.04 V;
- The current values are calculated using the standard algorithm: I1 = U12/R1 = 0.52 A, I2 = U12/R2 = 0.26 A;
- summation checks the correctness of the calculations: I = I1 + I2 = 0.52 + 0.26 ≈ 0.8 A.
Example 2 (mixed method of connecting resistors):
- current in this version is 1.2 A;
- the voltage in the section with a group of parallel resistors is Uab = I * Reeq(12345) = 1.2*2.5 = 3V;
- By analogy with the previous example, it is easy to calculate the current in each individual branch: I12 = Uav/(R1 + R2) = 3/ (15 + 5) = 0.15 A;
- I3 = Uav/ R3 = 3/ 5 = 0.6 A;
- I4 = Uav/ R4 = 3/ 10 = 0.3 A;
- I5 = Uav/ R5 = 3/20 = 0.15 A;
- according to the rule of equality of currents at the input and output of the node, the correctness of the calculations made is checked: I = I12 + I3 + I4 + I5 = 0.15 + 0.6 + 0.3 + 0.15 = 1.2 A.
Parallel power
To correctly select resistive components in electrical circuits, power dissipation must be taken into account. This parameter (P) is calculated using the classic formula P = U (voltage at the terminals, V) * I (current in the circuit, A). It indirectly determines the energy that is spent on heat generation. Proportions also apply:
P = I2 *R = U2/ R.
For your information. The design of each element is designed for a specific operating temperature range. Exceeding the threshold can destroy the part, the soldering point, and neighboring components. One should not forget about a simultaneous significant change in resistance, which can disrupt the functional state of the electrical circuit.
For the calculation, select a suitable formula taking into account the known initial parameters (data from example 2 in the previous section):
- current – 1.2 A;
- at resistance R6=7.5 Ohm the power dissipation will be: P6 = I2 *R = 1.44 * 7.5 = 10.8 W;
- It is difficult to find such a resistor, since the standard range offers ratings from 0.05 to 5 W;
- in another circuit (R5=20 Ohm) the calculated current will be 0.15 A, so P5= 0.0225 * 20 = 0.45 W;
- in this case, you can choose a product with a suitable dissipation power in the standard range of 0.5 W (experts recommend making a 1.52-fold margin, so it is better to use a 1 W resistor).
Standard symbols on electrical diagrams and typical power ratings
For your information. When choosing resistors, you should take into account the product class in terms of electrical resistance accuracy. In serial parts, deviations of 5-20% are acceptable.
How to find resistance in parallel connection
To calculate this parameter, use the following formulas:
- 1/G;
- U/I;
- U2/P;
- P/I2.
Select the appropriate option (combination) taking into account the available initial data. It should be remembered that there is a single voltage at the input and output and different currents in individual branches. Computing technology is discussed in previous sections.
Winding process
How to wind a coil for an electronic cigarette? Let's look at this issue using a standard coil as an example. Art coils are complex in their implementation, so it’s unlikely to be possible to explain anything briefly.
Here is a list of tools that we will need in our work:
- scissors;
- tweezers (preferably ceramic);
- pliers;
- screwdriver (it can also be used for winding);
- wire cutters
So, let's take a closer look at the process itself:
- In any task, hygiene is important, so it is necessary to wash your hands and tools. First of all, this is necessary so that the cotton wool for the wick does not absorb foreign aromas;
- If the wire material twists or springs, you need to burn it (you can use a gas stove or a lighter). This paragraph does not apply to nickel and titanium. Under no circumstances should you burn them - you will not only reduce the quality, but also contribute to the release of harmful substances;
- The wire must be degreased with alcohol. If you are using nickel or titanium, this step must be performed before winding, as they are not allowed to be burned through;
- Take a screwdriver or a special winding tool and start winding the wire around. Depending on the type of winding chosen, the turns should be made tightly to each other or leave a space of about 1 mm between them. Don’t worry if they turn out uneven, it will all be corrected later;
- After a sufficient number of turns have been made, they can be compressed with pliers and then slightly stretched;
- Now we can proudly declare that the spiral is ready. Let's proceed to installing this spiral on the base of the clear. Unscrew the coil screws and insert the ends of the coil under them. Then tighten the bolts back. Using a screwdriver, adjust the spiral again so that it is positioned exactly in the center. Make sure that its edges do not come into contact with the walls of the base. The ends of the wire should also not touch the base elements; excess must be removed with wire cutters. Otherwise, a short circuit may occur;
- Important! The higher the spiral is in relation to the lower hole, the greater the blow to the throat, and vice versa;
- Press the hover button to burn through the already installed coil. It should turn red evenly from the center to the edges. If any area does not heat up, run ceramic tweezers over it;
- The final step is to place the cotton wool or other material of your choice into the spiral. The cotton wool should pass freely from one side to the other;
- Cut off the long tails, leaving a little in reserve;
- Hide the remaining ends inside the clearomizer base. Make sure that the cotton wool does not get on the threads.
Online calculator for parallel connection of resistors
It is not difficult to manually calculate the series connection of resistors. But for parallel and combined circuits it is more convenient to use a calculator. The corresponding services are offered free of charge by reference and thematic websites.
Specialized modern software provides automated calculation of operating parameters of complex circuits. The user can:
- rearrange conductors;
- install LEDs, capacitors, and other components in the right place;
- change the input signal.
Application “simulator” of electrical circuits for mobile devices on Android OS
The information presented in the publication will be useful for independent calculations and checks. It will help you choose a resistor in the store and restore the functionality of the electrical device.
Types of conductors
The conductivity of an electric current by a substance is associated with the presence of free charge carriers in it. Their number is determined by their electronic configuration.
Read also: Specific heat of fusion of brass
To do this, you need a chemical formula of the substance, with which you can calculate their total number. The value for each element is taken from the periodic table of Dmitri Ivanovich Mendeleev.
Electric current is the ordered movement of free charge carriers, which are affected by an electromagnetic field. When current flows through a substance, a stream of charged particles interacts with the nodes of the crystal lattice, and part of the kinetic energy of the particle is converted into thermal energy. In other words, the particle “hits” the atom and then continues moving again, picking up speed under the influence of the electromagnetic field.
The process of interaction of particles with nodes of the crystal lattice is called electrical conductivity or resistance of the material. The unit of measurement is Ohm, and it can be determined using an ohmmeter or calculated. According to the property of conductivity, substances can be divided into 3 groups:
- Conductors (all metals, ionized gas and electrolytic solutions).
- Semiconductors (Si, Ge, GaAs, InP and InSb).
- Non-conductors (dielectrics or insulators).
Conductors always conduct electric current because they contain free electrons, anions, cations and ions in their atomic structure. Semiconductors conduct electricity only under certain conditions, which affect the presence or absence of free electrons and holes. Factors affecting conductivity include the following: temperature, illumination, etc.
Dielectrics do not conduct electricity at all, since there are no free charge carriers in their structure. When performing calculations, every radio amateur must know the dependence of resistance on certain physical quantities.
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