Parallel and serial connection. Serial and parallel connection of conductors

In physics we study the topic of parallel and serial connection, and it can be not only conductors, but also capacitors. It is important not to forget how to look each of them in the diagram. And then apply a specific formula. They need to memorize.

How to distinguish between these two compounds?

Please look Carefully at the diagram. If the wires to represent how the road, the car on it will play the role of resistors. On a straight road without any ramifications of the cars go one after another in a chain. It looks exactly the same and the serial connection of conductors. The road in this case can have an unlimited number of turns, but no intersection. No matter how wags the road (wires), machinery (resistors) are always arranged one behind the other, on the same chain.

Quite another matter, if we consider the parallel connection. Then the resistors can be compared with the athletes at the start. They stand each on its own track, but the direction of movement is the same, and finish in one place. Similarly, the resistors — each with its own wire, but they are all connected at some point.

Formula for amperage

It always is the theme of “Electricity”. Parallel and series connections of different effects on the magnitude of the current in the resistors. For them, the formulas that you can memorize. But simply remember the meaning that is embedded in them.

So, the current at consecutive connection of conductors is always the same. That is, each value of current strength is no different. To draw an analogy, if you compare the wire with the pipe. In it, the water always flows in the same way. And all the obstacles in her way will smejatsja with the same force. Same with amperage. Therefore, the formula for total current in the circuit with the series connection of resistors looks like this:

Recommended

"Knowledge is light and ignorance is darkness": the value, meaning and alternatives

There are some sayings that would seem to need no explanation, such as “teaching & ndash; light and ignorance – darkness”. But some still do not understand their meaning. But not only for such people is written by our article. I...

What was invented by Mendeleev for the army. The history and fate of the invention

D. I. Mendeleev was a brilliant Russian scientist-polymath, who made many important discoveries in various fields of science and technology. Many people know that he is the author of “Fundamentals of chemistry" and the periodic law of chem...

The origin of the Slavs. The influence of different cultures

Slavs (under this name), according to some researchers, appeared in the story only in 6 century ad. However, the language of nationality bears the archaic features of the Indo-European community. This, in turn, suggests that the origin of the Slavs h...

I _Total = I ₁ = I ₂

Here the letter I denotes the current. That's a common abbreviation, so you need to remember.

Current with parallel connection will not be constant. With the same analogy with a pipe it turns out that water is split into two streams, if the pipe will spin off. The same phenomenon is observed with shock when, on his way there the branching wires. The formula for total current in parallel conductors:

I _Total = I ₁ + I ₂

If the fork is composed of wires, which is more than two, then in the above formula, the same number will be greater terms.

Formulas for stress

When one considers the scheme, which made the connection conductors in series, the voltage of the entire site is determined by the sum of these values at each particular resistor. Compare this situation with the plates. To keep one of them get easily to one person, the second side he'll take, but with difficulty. To hold three plates next to each other one person will not succeed, you will need the help of a second. And so on. The efforts of the people added.

The Formula for total voltage plot of the circuit with the series connection of the conductors looks like this:

U _Total = U ₁ + U ₂, where U is the designation adopted for the electric voltage.

Another situation occurs if we consider the parallel connection of resistors. When the plates are placed on each other, they can still hold one person. Therefore, folding don't have. The same analogy is observed with a parallel connection of conductors. The voltage on each of them the same and equal to that on all of them at once. The formula for the total voltage is:

U _Total = U ₁ = U ₂

The Formulas for electrical resistance

They already can not remember, and know the formula of Ohm's law and from it to deduce the desired. From the law it follows that the voltage is equal to the product of current and resistance. That is, U = I * R, where R-the resistance.

Then the formula that you want will work, depends on how connected conductors.

• Consistently, so, we need equality for stress — the I_Total * R_Total = I₁ * R₁ + I₂ * R_2;
• In parallel, you must use the formula for amperage — the U_Total / R_Total = U₁ / R₁ + U₂ / R₂ .

Then follow simple conversion, based on the fact that in the first equality of all the current have the same value, and the second — voltages are equal. So, they could be reduced. That is, are these expressions:

1. R _Total = R ₁ + R ₂ (for serial connection of conductors).
2. 1 / R _Total = 1 / R ₁ + 1 / R ₂ (with parallel connection).

Increasing the number of resistors included in a network, changing the number of summands in these expressions.

It is Worth noting that the parallel and series connection of conductors of different effects on the total resistance. The first of them reduces the resistance of the chain. And it is less than the smallest of the used resistors. Whenseries connection of all logical values are added, so the total number will always be the largest.

Current

The last three values are the laws of parallel connection and serial arrangement of the conductors in the circuit. Therefore, they know must. About the work and power you just need to remember the basic formula. It is written like this: A = I * U * t And — current, t-time of its passing through a conductor.

To determine the total work of a series connection you need to replace in the original expression strain. Get the equality: A = I * (U ₁ + U ₂) * t, opening the brackets in which will that work on the whole area equals the sum of each specific consumer current.

Similarly, goes the argument, if the scheme of parallel connection. Only supposed to replace the current. But the result is the same: A = A ₁ + A ₂.

Current Capacity

In deriving the formula for power (symbol “R”) part of the circuit again you need to use one formula, P = U * I. After these considerations, it turns out that parallel and serial connections are described by the formula for power P = P ₁ + P ₂.

That is, no matter how schemes, the total capacity will consist of those who are involved in the work. This explains the fact that it is impossible to include in the network of the apartment at the same time powerful devices. It simply can not stand such a load.

How does the connection of conductors for repair Christmas lights?

Immediately after will burn out one of the bulbs, it will become clear how they were connected. A series connection will be off any of them. This is because came into disrepair lamp creates a gap in the circuit. So you need to check everything to determine what is blown, replace it and the garland will work.

If it is a parallel connection, it does not stop working when a fault of one of the light bulbs. Because the circuit is fully broken, and only one parallel part. To fix such a garland, no need to check all the circuit elements, and only those who don't glow.

What happens to the chain if it includes no resistors, and capacitors?

In their series connection there is the situation: charges from the pros the power source comes only on the outer lining of extreme capacitors. Those that are in between, just pass this charge along the chain. This explains the fact that all the plates appear the same charges but have different signs. Therefore, the electric charge of each capacitor, connected in series, we can write this formula:

Q _Total = q ₁ = q ₂.

To determine the voltage on each capacitor will require knowledge of the formula: U = q / C. In it — the capacitance of the capacitor.

The Total voltage is subject to the same law, which is valid for resistors. Therefore, replacing in the formula of capacitance the voltage of the sum, we get that the total capacity of the appliances need to be calculated by the formula:

C = q / (U ₁ + U ₂).

To Simplify this formula, turning fractions, and replacing the ratio of voltage-to-charge capacity. It is the equality: 1 / S = 1 / S ₁ + 1 / S ₂.

Somewhat different is the situation when the connection of capacitors — parallel. Then the total charge is determined by the sum of all charges that accumulate on the plates of all devices. But the voltage value continues to be determined under the General laws. Therefore, the formula for total capacitance of parallel-connected capacitors is:

With = (q 1 + q 2 ) / U.

That is, this value is considered as the sum of each of the used devices connection:

C = C ₁ + S _2.

How to determine the total resistance of an arbitrary connection of conductors?

That is, one in which successive areas alternate with parallel and Vice versa. They are still fair all the laws. Only need to apply them in stages.

First supposed to mentally expand the scheme. If you imagine it, then you need to draw what comes out. The explanation will become clearer when considered on a concrete example (see figure).

It is convenient to start drawing with points B and C. They must be put at some distance from each other and from the edges of the sheet. On the left, to point B, one wire, and aimed right for two. Point In contrast, the left has two branches, and after it is a single wire.

Now you need to fill the space between these points. The upper wire should be placed three resistor ratios of 2, 3 and 4, and the bottom will go the one whose index is 5. The first three are connected in series. With the fifth resistor they are parallel.

The Remaining two resistors (first and sixth) is connected in series with the section BC. So figure you can simply add the two rectangles on either side of the selected points. It remains to apply the formula to calculate resistance is:

• First, that which is provided for serial connection;
• Then forparallel;
• And again for consistent.

Similarly, you can deploy any, even very complex scheme.

The challenge for the conductor series connection

A Condition. In a circuit to each other connected to two lamps and a resistor. The total voltage is 110 V and current of 12 A. What is the resistance of the resistor, if each lamp is designed to stress the 40 In?

Decision. Since this is a serial connection, the formula of its laws are known. It is only necessary to apply them. To begin with, to find out the voltage that falls on the resistor. To do this, the total you need to subtract twice the voltage of one lamp. It turns out 30.

Now that you know two quantities, U and I (the second of them given in the condition, because the total current is the current in each successive user), you can count the resistance of the resistor according to Ohm's law. It is equal to 2.5 Ohms.

Answer. the resistance of the resistor is equal to 2.5 Ohms.

Task connection of capacitors in parallel and series

Condition. There are three condenser with capacities of 20, 25 and 30 UF. Determine their total capacitance in series and parallel connection.

Decision. Easier to start with a parallel connection. In this situation, all three values need to fold. Thus, the total capacity is equal to 75 UF.

The more complicated calculations will be a series connection of these capacitors. After all, you first need to find the relationship of units to each of these containers, and then stack them with each other. It turns out that unit divided by the total capacity equal to 37/300. Then the desired value is obtained approximately 8 UF.

Answer. the Total capacity of a series connection of 8 µf, in parallel — 75 UF.