In physics, the topic of parallel and serial connection is studied , and this can be not only conductors, but also capacitors. It is important here not to get confused in how each of them looks in the diagram. And then apply specific formulas. By the way, they need to be remembered by heart.
How to distinguish between these two compounds?
Look carefully at the diagram. If the wires are presented as a road, then the cars on it will play the role of resistors. On a straight road, without any branching, cars go one after another in a chain. The serial connection of conductors also looks the same. The road in this case can have an unlimited number of turns, but not a single intersection. No matter how the road (wires) wag, the cars (resistors) will always be located one after another, in one chain.
A completely different matter if parallel connection is considered. Then the resistors can be compared with the athletes at the start. They each stand on their own path, but they have the same direction of movement, and the finish in one place. So are the resistors - each of them has its own wire, but they are all connected at some point.
Formulas for Current
It is always discussed in the topic "Electricity". Parallel and serial connection differently affect the magnitude of the current in the resistors. For them, formulas that can be remembered are derived. But just remember the meaning that is embedded in them.
So, the current in the series connection of the conductors is always the same. That is, in each of them the value of the current strength does not differ. An analogy can be made if we compare the wire with the pipe. In it, water flows always the same. And all the obstacles in her path will be swept away with the same force. Also with amperage. Therefore, the formula for the total current in a circuit with a series connection of resistors looks like this:
I total = I 1 = I 2
Here, the letter I denotes the current strength. This is a common designation, so you need to remember it.
The current in parallel connection will no longer be a constant value. With the same analogy with a pipe, it turns out that the water will be divided into two streams if the main pipe has a branch. The same phenomenon is observed with current when a branching of wires appears in its path. The formula for the total current strength in parallel connection of conductors :
I total = I 1 + I 2
If the branching is composed of wires, which are more than two, then in the above formula the same number will be more terms.
Formulas for stress
When a circuit is considered in which the connection of the conductors is performed in series, the voltage over the entire section is determined by the sum of these values on each specific resistor. Compare this situation with the plates. It is easy for one person to keep one of them; he can also take the second next, but with difficulty. It is no longer possible for one person to hold three plates next to each other, the help of the second will be required. And so on. The efforts of people add up.
The formula for the total voltage of a circuit section with a series connection of conductors looks like this:
U total = U 1 + U 2 , where U is the designation adopted for voltage.
Another situation arises if parallel connection of resistors is considered. When plates are stacked on top of each other, one person can still hold them. Therefore, you do not have to add anything. The same analogy is observed with parallel connection of conductors. The voltage on each of them is the same and equal to that on all of them at once. The general voltage formula is as follows:
U total = U 1 = U 2
Formulas for electrical resistance
They can no longer be memorized, but know the formula of Ohm's law and derive the necessary one from it. From this law it follows that the voltage is equal to the product of current strength and resistance. That is, U = I * R, where R is the resistance.
Then the formula with which it will be necessary to work depends on how the connection of the conductors is made:
- sequentially, it means equality for voltage is needed - I total * R total = I 1 * R 1 + I 2 * R 2;
- in parallel, it is necessary to use the formula for the current strength - U total / R total = U 1 / R 1 + U 2 / R 2 .
The following are simple transformations, which are based on the fact that in the first equality all current forces have the same value, and in the second - the voltages are equal. So, they can be reduced. That is, the following expressions are obtained:
- R total = R 1 + R 2 (for series connection of conductors).
- 1 / R total = 1 / R 1 + 1 / R 2 (with parallel connection).
With an increase in the number of resistors that are included in the network, the number of terms in these expressions changes.
It is worth noting that parallel and serial connection of conductors differently affect the overall resistance. The first of them reduces the resistance of the circuit. Moreover, it turns out to be smaller than the smallest of the resistors used. With a serial connection, everything is logical: the values add up, so the total number will always be the largest.
Work current
The previous three values are the laws of parallel connection and sequential arrangement of conductors in a circuit. Therefore, you need to know them. About work and power, you just need to remember the basic formula. It is written as follows: A = I * U * t , where A is the work of the current, t is the time of its passage through the conductor.
In order to determine the overall work in series connection, it is necessary to replace the voltage in the original expression. The result is the equality: A = I * (U 1 + U 2 ) * t, opening the brackets in which it turns out that the work on the entire site is equal to their sum on each specific current consumer.
The reasoning is similar if parallel circuit design is considered. Only replace relies on amperage. But the result will be the same: A = A 1 + A 2 .
Current power
When deriving the formula for the power (designation "P") of the circuit section, one again needs to use one formula: P = U * I. After similar reasoning, it turns out that the parallel and serial connections are described by such a formula for power: P = P 1 + P 2 .
That is, no matter how the schemes were drawn up, the total capacity will consist of those that are involved in the work. This explains the fact that it is impossible to include many powerful appliances at the same time in the apartment network. She just can not stand such a load.
How does the connection of conductors to repair the New Year's garland?
Immediately after one of the bulbs burns out, it becomes clear how they were connected. When connected in series, none of them will glow. This is due to the fact that a damaged lamp creates a gap in the circuit. Therefore, you need to check everything to determine which burned out, replace it - and the garland will work.
If a parallel connection is used in it, then it does not stop working if one of the bulbs fails. After all, the chain will not be completely broken, but only one parallel part. To repair such a garland, you do not need to check all the elements of the chain, but only those that do not glow.
What happens to a circuit if capacitors are not included in it, but resistors?
When they are connected in series, the following situation is observed: charges from the pluses of the power source arrive only on the outer plates of the extreme capacitors. Those in between simply transmit this charge in a chain. This explains the fact that on all plates the same charges appear, but with different signs. Therefore, the electric charge of each capacitor connected in series can be written as follows:
q total = q 1 = q 2 .
In order to determine the voltage across each capacitor, you need knowledge of the formula: U = q / C. In it, C is the capacitance of the capacitor.
The total voltage obeys the same law that is valid for resistors. Therefore, replacing the voltage in the capacity formula by the sum, we get that the total capacity of the devices must be calculated by the formula:
C = q / (U 1 + U 2 ).
This formula can be simplified by flipping fractions and replacing the ratio of voltage to charge by capacity. It turns out this equality: 1 / C = 1 / C 1 + 1 / C 2 .
The situation when the connection of the capacitors is parallel is somewhat different. Then the total charge is determined by the sum of all charges that accumulate on the plates of all devices. And the voltage value is still determined according to general laws. Therefore, the formula for the total capacitance of parallel-connected capacitors looks like this:
C = (q 1 + q 2) / U.
That is, this value is considered as the sum of each of the devices used in the connection:
C = C 1 + C 2.
How to determine the total resistance of an arbitrary connection of conductors?
That is, one in which successive sections are replaced by parallel ones, and vice versa. For them, all the laws described are still valid. Only they need to be applied in stages.
First, it is supposed to mentally expand the scheme. If it is difficult to imagine it, then you need to draw what is obtained. The explanation will become clearer if we consider it with a specific example (see. Figure).
It is convenient to start drawing it from points B and C. They must be placed at some distance from each other and from the edges of the sheet. On the left, one wire approaches point B, and two are directed to the right. Point B, on the contrary, has two branches on the left, and after it there is one wire.
Now you need to fill the space between these points. Three resistors with coefficients 2, 3 and 4 must be placed along the top wire, and the bottom one with the index equal to 5. The first three are connected in series. With the fifth resistor, they are parallel.
The remaining two resistors (first and sixth) are connected in series with the considered portion of the BV. Therefore, the picture can simply be supplemented with two rectangles on either side of the selected points. It remains to apply the formulas for calculating the resistance:
- first the one given for serial connection;
- then for parallel;
- and again for consistent.
In this way, you can deploy any, even very complex scheme.
The task of the serial connection of conductors
Condition. Two lamps and a resistor are connected in a circuit one after another. The total voltage is 110 V and the current is 12 A. What is the resistance of the resistor if each lamp is rated for 40 V?
Decision. Since a sequential compound is considered, the formulas of its laws are known. It is only necessary to apply them correctly. To begin with, to find out the value of the voltage that falls on the resistor. To do this, from the total you need to subtract twice the voltage of one lamp. It turns out 30 V.
Now that two quantities are known, U and I (the second of them is given in the condition, since the total current is equal to the current in each serial consumer), we can calculate the resistance of the resistor according to Ohm's law. It turns out to be 2.5 ohms.
Answer. The resistance of the resistor is 2.5 ohms.
The task of connecting capacitors, parallel and serial
Condition. There are three capacitors with capacitances of 20, 25 and 30 uF. Determine their total capacitance in series and parallel connection.
Decision. It’s easier to start with a parallel connection. In this situation, all three values just need to be added. Thus, the total capacitance is 75 μF.
Somewhat more complicated calculations will be with a series connection of these capacitors. After all, you first need to find the relationship of a unit to each of these containers, and then add them together. It turns out that the unit divided by the total capacity is 37/300. Then the desired value is approximately 8 μF.
Answer. The total capacitance with a serial connection of 8 μF, with a parallel - 75 μF.