Electricity. Units of electrical capacity. Capacitors. Electrical capacity of a reinforced conductor. Mutual capacitance of two conductors Capacitors For a charged and reinforced conductor, it is sure to be solidified

Formulas (94.3), (94.5) and (94.7) show that the capacity of capacitors of any form is directly proportional to the dielectric penetration of the dielectric, which fills the space between the plates. Therefore, the drying out of ferroelectrics significantly increases the capacitance of capacitors.

Capacitors are characterized breakdown voltage- the difference in potential between the plates of the capacitor, which is subject to try- Electric discharge through a dielectric ball in a capacitor. The disruptive voltage lies under the shape of the plates, the power of the electrician and the other.

To increase the capacity and increase the possible value of the capacitors, connect them to the battery, in which case they are connected in parallel and in series.

1. Parallel connection of capacitors(Fig. 144). For parallel-connected capacitors, the potential difference on the plates of the capacitors is the same and the same j A -j B. What are the capacitances of the surrounding capacitors? Z 1 , W 2 , ..., Z n , then, okay (94.1), their charges will increase

Q 1 = C 1 (j A -j B),

Q 2 =C 2 (j A -j B),

Q n = З n (j A -j B), and the charge of the capacitor bank

Full battery capacity

i.e., when capacitors are connected in parallel, the sum of the capacitances of the adjacent capacitors is equal.

2. Serial connection of capacitors(Fig. 145). In series-connected capacitors, the charges of all plates are equal in modulus, and the difference in potentials on the battery charge

where are the capacitors that can be seen

On the other hand,

Then, when capacitors are connected in series, the values ​​of the capacitances are calculated. Thus, when capacitors are connected in series, the resulting capacity Z Always less than the lowest capacity that is available in the battery.

All speeches can be divided into two groups – conductors and dielectrics. Before dielectrics are mentioned, there are no strong electrical charges in the warehouse. Such words include, for example, ceramics, glass, gum and others. Speeches are sent to the conductors, to the warehouses of which free charges are included. Before such speeches lie metals, electricity and others.

If a charge is given to the reinforced conductor, it will distribute over the surface of the conductor so that the field strength in the middle of the conductor is equal to zero. The nature of the distribution of the charge lies in the charge itself, and lies in the shape of the conductor and squeezes the excess conductor of the middle. A new charge is distributed over the surface of the conductor, similar to the previous charge. Thus, with an increase in the charge that is applied to the conductor at a time, the surface density of the charge and the charge that falls on one area of ​​the surface of the conductor will also increase by a factor at any point on the surface of the conductor. In this way, you can write:

(1)

Here - the surface strength of the charge - is a function of the coordinates of the surface point that is being looked at.

To calculate the field potential created by a charged conductor, we divide the surface of the conductor flat (Fig. 1) onto infinitely small surface elements that carry a charge equal to

(2).

The potential of the electrostatic field created by one of these point charges, at point A (Fig. 1), which is located in front of it, is calculated by the formula:

(3)

Here Nm 2 / Cl 2 - constant, which is indicated by the choice of system one; F/m – electrostatic has become vacuum; - dielectric penetration of the middle, which is the source of the conductor.

To find the potential of the electrostatic field created by the entire charged surface of the conductor at point A, you need to integrate formula (3) over the entire surface of the conductor. Since the surface of the conductor is always closed, we can eliminate:

(4)

Integral for a given surface there is a constant number. Splinters size for tasks of minds it is also stationary, then, as can be seen from formula (4), the potential of the electrostatic field created by the reinforced conductor at the given point is proportional to its charge.

The physical quantity that corresponds to the charge of the conductor up to its potential is called the electrical capacity of the reinforced conductor.

We substitute formula (5) formula (4) and remove:

(6)

Formula (6) shows that the electrical capacity of a reinforced conductor depends on its shape, size and dielectric penetration of the core in which the conductor is located. The result is that geometrically similar conductors contain capacitances that are proportional to their linear dimensions. In addition, formula (6) shows that the electrical capacity of the conductor does not depend on its charge or potential.

If the electrical charge of the conductor increases by an amount, its potential increases by an amount, then it follows from formula (5):

(7)

In such a manner

(8)

From formula (8) it is clear that the electrical capacity of the conductor shows what charge needs to be given to the conductor in order to change one unit of potential (in the system there are units of CI per 1 volt).

Samotnіm called a conductor, extending the table far from other bodies so that the infusion of charges and fields of other bodies can be obtained. When such a conductor is exposed to a certain charge, the veins spread out on its surface so that the minds are equalized. In the extra space, the charge of the conductor creates an electric field. If an infinitely small charge (does not flow onto the charge of the conductor) is transferred to the surface of the conductor, then the field forces act on the robot. The installation gives the potential of the conductor, which adds inheritance to the charge.

If the conductor additionally imparts a charge, another portion of the charge will spread over the surface just like the first portion. It is obvious that at all points in space the electric field strength will double. As the robot grows, so does the potential of the conductor. In this manner, it appears that charge, information to the conductor, and the potential generated by it proportional . So you can write down the relationship:

Proportionality factor Z The relation (16.3) characterizes the ability of a conductor to accumulate an electric charge and is called the electrical capacity of a reinforced conductor. This conductor parameter vibrating with farads . An electrical capacity of 1 farad contains a conductor, which, when charged with a charge of 1 coulomb, rises to a potential of 1 volt..

We expand the capacity of a water-reinforced spherical conductor, which has dielectric penetration in the middle. The field strength of a charged sphere between the spaces is described by a expression similar to the expression for the field strength of a point charge located in the center of the sphere. Therefore, the way to work by moving a small point charge from the surface of the sphere to the radius that carries the charge is that it looks like it is infinite:

Tom electrical capacity of the reinforced sphere is indicated by viraz:

Substituting the radius of the Earth into (16.6), the electrical capacitance of the Earth becomes approximately 700 µF.

Capacitors

The powered conductors have a low capacity. However, technology uses devices that can produce electrical capacity of up to several farads. With such devices capacitors . The principle of capacitor control is based on the fact that when another (or uncharged) conductor is close to a charged conductor, the electrical capacity of the system increases significantly. The field of the strengthened conductor on the body that is approaching has induced charges, and the charges of the sign adjacent to the strengthened conductor grow closer and flow more strongly into its field. The potential of the conductor behind the module changes, and the charge is saved. Tse means that Your electricity capacity is growing.

The remote parts of the conductor that are close can be connected to the Earth (grounded) in order to induce a charge of the same sign as that of the connected conductor, distributing along the surface of the Earth and not flowing into the system potential. Obviously, by bringing the conductors being charged as close as possible, a significant increase in electrical capacity can be achieved. In general, capacitors are prepared flat , if the conductors are charged for a long time ( capacitor plates ) It looks like, for example, a smear of foil is covered with a thin ball of dielectric. In this case, the electric field of the system appears to be concentrated in the space between the plates, and external bodies do not flow into the capacitor capacity. You can also see linings in the form of concentric cylinders or spheres.

Electrical capacity of the capacitor, After the values, the value of the ratio of the charge of the skin from the plates to the difference in potentials between them is called:

Dielectric penetration of the material between the plates of the capacitor.

« Physics - 10th grade"

In what way can a great electric charge be accumulated on conductors?

By any method of electrifying bodies - by means of rubbing, an electrostatic machine, a galvanic cell, etc. - a particle of neutral body is charged as a result of which some of the charged particles pass from one body to another.
Call these particles e.g. electrons.

When two conductors are electrified, for example in an electrostatic machine, one of them receives a charge of +q, and the other -q.
An electric field is created between the conductors and a difference in potentials (voltage) occurs.
Due to the increased charge of the conductors, the electric field between them will increase.

In a strong electric field (with great stress and with great tension), the dielectric (for example, wind) becomes conductive.
Mozhliviy so ranks try dielectrics: a spark jumps between the conductors and they are discharged.
The less voltage between the conductors and the greater their charges, the greater the charge that can be accumulated on them.

Electricity.

We introduce a physical quantity that characterizes the ability of two conductors to accumulate an electric charge.
Call the quantity Qiu electrical.

The voltage U between two conductors is proportional to the electrical charges present on the conductors (on one +|q|, and on the other -|q|).
It’s true that as soon as the charges are added, the strength of the electric field will become 2 times greater, and therefore the voltage will be 2 times greater.

Therefore, the charge of one of the conductors (on the other there is the same charge behind the module) until the difference in potentials between this conductor and the conductor does not lie in the charge.

It is indicated by the geometric dimensions of the conductors, their shape and mutual rotation, as well as the electrical power of the superfluous center.

This allows you to understand the electrical capacity of two conductors.

The electrical capacity of two conductors is called the relationship between the charge of one of the conductors and the difference in potential between them:

The electrical capacity of a reinforced conductor is equal to the charge of the conductor up to its potential, since all other conductors are infinitely removed and the potential of an infinitely distant point is equal to zero.

The voltage U between conductors is lower when the charges +|q| i -|q|, the greater the electrical capacity of the conductors.

It is possible to accumulate large charges on conductors without causing a dielectric breakdown.
However, the electrical capacity itself cannot be kept up neither by the charge conductors, nor by the voltage that arises between them.

Units of electrical capacity.

Formula (14.22) allows you to supply one unit of electrical capacity.

The electrical capacity of the two conductors is numerically equal to units, when the charges are removed+1 Cl і-1 Kl there is a difference in potential between them 1 Art.

Call one Qiu farad(F); 1 F = 1 C/st.

Because the charge of 1 C is even greater, the capacity of 1 F appears to be even greater.
Therefore, it is practical to often use parts of this unit: microfarad (μF) - 10 -6 F and picofarad (pF) - 10 -12 F.

An important characteristic of conductors is electrical capacity.
The electrical capacity of the conductors is greater than the difference in potentials between them when the charges of the adjacent signs are reduced.

Capacitors.

You can see a conductor system with very high electrical capacity in any radio or buy it in a store. It's called a capacitor. You will immediately find out how such systems are controlled and where their electrical capacity is stored.

The systems with two conductors, called capacitors. The capacitor has two conductors separated by a dielectric ball, the size of which is small compared to the size of the conductors. In this case, guides are called linings capacitor.

The simplest flat capacitor consists of two parallel plates, which are located on a small side, one side of the other (Fig. 14.33).
Since the plates are charged behind the module and lie behind the sign, the power lines of the electric field begin at the positively charged capacitor plate and end at the negatively charged (Fig. 14.28). That's why the whole electric field concentrated in the middle of the capacitor and uniformly.

To charge the capacitor, it is necessary to attach its plate to the poles of the voltage generator, for example, to the poles of the battery. You can also connect one plate to the battery pole, which has the other grounding pole, and ground the other plate of the capacitor. Then the grounded plate will lose a charge that is equal to the charge of the ungrounded plate. This same charge behind the module goes into the ground.

Pid capacitor charge This means that the charge on one of the plates is absolutely not significant.

The electrical capacity of the capacitor is determined by formula (14.22).

Electric fields in excess bodies do not penetrate the middle of the capacitor and do not affect the difference in potential between the plates. Therefore, it is practically impossible for the electrical capacity of the capacitor to lie hidden near any other bodies.

Electrical capacity of a flat capacitor.

The geometry of a flat-plate capacitor is determined by the area of ​​its plates and the distance between them. These values ​​determine the capacitance of a flat-plate capacitor.

The larger the area of ​​the plates, the greater the charge that can be accumulated on them: q~S. On the other hand, the voltage between the plates is determined by the formula (14.21) of the proportional distance d between them. Therefore there is amnesty

In addition, the capacity of the capacitor lies under the influence of the insulator between the plates. If the dielectric fragment weakens the field, then the electrical capacity due to the dielectric will increase.

Let's reconsider the truth of the delay, which we have taken away from the world. For this we take a capacitor, whose space between the plates can be changed, and an electrometer with a grounded housing (Fig. 14.34). We connect the body and stem of the electrometer with the capacitor plates, conductors and a chargeable capacitor. To do this, you need to push the electrified stick of the capacitor plate connected to the rod. The electrometer will show the difference in potential between the plates.

Rozsuvayuchi plates, mi viyavimo increased difference in potentials. Based on the calculated electrical capacity (formula (14.22)), this indicates a change. It is certain that the electrical capacity must change due to the increased distance between the plates.

By inserting a dielectric plate, for example, an organic glass, between the plates of the capacitor, we can clearly Change in potential difference. Otje, The electrical capacity of a flat capacitor increases over time. Stand between the plates d can be even smaller, and the area S can be large. Therefore, with small dimensions, the capacitor can cause high electrical capacity.

To put it in perspective: the dielectric strength between the plates of a flat capacitor with an electrical capacity of 1 F and the distance between the plates d = 1 mm is due to almost the area of ​​the plates S = 100 km 2 .

In addition, the capacity of the capacitor lies under the influence of the insulator between the plates. Since the dielectric weakens the field, the electrical capacity of the dielectric increases: de-electric penetration of the dielectric.

Serial and parallel connection of capacitors. In fact, capacitors are often connected in different ways. Presented on the little one 14.40 sequential connection three capacitors.

If points 1 and 2 are connected to the voltage source, then the left plate of capacitor C1 will transfer charge +qy to the right plate of capacitor S3 - charge -q. As a result of electrostatic induction, the right plate of capacitor C1 has a charge -q, the fragments of the plates of capacitors C1 and C2 are connected and before connecting the voltage was electrically neutral, then the law of conservation of charge on the left plate of capacitor C2 appears charge +q i etc. All capacitor plates connected in this way will have a new charge behind the module:

q = q1 = q2 = q3.

Calculate the equivalent electrical capacity - this means calculating the electrical capacity of such a capacitor, which, at the same potential difference, accumulates the same charge q as the capacitor system.

The difference in potentials φ1 - φ2 is the sum of the difference in potentials between the plates of the skin and capacitors:

φ 1 - φ 2 = (φ 1 - φ A) + (φ A - φ B) + (φ B - φ 2),
or U = U 1 + U 2 + U 3.

Using formula (14.23), we can write:

A diagram is presented for the baby 14 41 parallel connections capacitors The potential difference between the plates of all capacitors is, however, the same:

φ 1 - φ 2 = U = U 1 = U 2 = U 3.

Charges on capacitor plates

q 1 = C 1 U, q 2 = C 2 U, q 3 = C 3 U.

On an equivalent capacitor with an equivalent charge on the plates at the same potential difference

q = q1 + q2 + q3.

For electrical capacity, using formula (14.23) we write: C eq U = C 1 U + C 2 U + C 3 U, also, C eq = C 1 + C 2 + C 3 i in the zagal form

Different types of capacitors.

Regardless of their purpose, capacitors are installed in different devices. A basic technical paper capacitor is made up of two pieces of aluminum foil, insulated on one side of the metal body with paper strips soaked in paraffin. The creases and stitches are tightly curled in a small package.

In radio technology, capacitors of replaceable electrical capacity are widely used (Fig. 14.35). Such a capacitor consists of two systems of metal plates, which, when the handles are wrapped, can fit one to the other. In this case, the flat parts of the plates change, they overlap, and, therefore, their electrical capacity. The dielectric in such capacitors is primarily used.

A significant increase in electrical capacity with the help of an additional change in the distance between the plates is achieved in electrolytic capacitors (Fig. 14.36). Their dielectric is a very thin layer of oxides that covers one of the plates (foil). The other cover is a paper, leaked with a special speech (electrolyte).

Capacitors allow you to store an electrical charge. The electrical capacity of a flat-plate capacitor is proportional to the area of ​​the plates and there is a proportional distance between the plates. In addition, it must lie under the influence of the electrical power between the plates.

Take a small empty metal bag and put it on the electrometer (Fig. 66). Using a test bag, in equal portions, transfer the charges from the bag of the electrophoretic machine to the bag, pushing the charged bag onto the inner surface of the bag. It is noted that with an increased charge on the coolant, the potential of the remaining energy to the Earth also increases. Precise research has shown that the potential of a conductor of any form is directly proportional to the magnitude of its charge. In other words, if the charge of the conductor will be q, 2q, 3q, ..., nq, then its potential will likely be φ, 2φ, 3φ, ..., nφ. The ratio of the charge of the conductor to its potential for a given conductor is a constant value:

If we take a similar relationship for a conductor of a different size (div. Fig. 66), it will also be constant, but with different numerical values. The value indicated by these settings is called the electrical capacity of the conductor. Conductor electrical capacity

A scalar quantity that characterizes the power of a conductor to absorb an electrical charge and a charge that moves the potential of the conductor by one is called electrical capacity. Electrocapacity is a scalar quantity. Since one conductor has an electrical capacity ten times greater than the other, then, as can be seen from the formula for electrical capacity, in order to charge them to the same potential, it is necessary for the first conductor to carry a charge ten times greater, not f another. Because of what has been said, it is clear that Electrical capacity characterizes the power of conductors to accumulate a greater or lesser charge depending on the balance of their potentials.

Where should the electrical capacity of a reinforced conductor be stored? To understand this, we take into account two differences in the value of the metal and empty coolers, as measured by the electrometer. With the help of a test bag, we charge the balls so that the values ​​of q charges remain the same. Bachimo, with whom the potential of the bags is not the same. A hole with a smaller radius was charged to a higher potential φ 1 and a hole with a larger radius (its potential φ 2). Because charge a sack of the same size q = C 1 φ 1і q = З 2 φ 2, A φ 1 >φ 2, That Z 2 >Z 1. To mean The electrical capacity of a reinforced conductor depends on the size of its surface: the larger the surface of the conductor, the greater its electrical capacity. This storage is explained by the fact that it is not the outer surface of the conductor that is charged. The electrical capacity of the conductor lies in its material.

We install one type of electrical capacity of the conductor in the CI system. For which the formula for electrical capacity has substitutable values q = 1 toі φ = 1 in:

One unit of electrical capacity - a farad - is taken to be the electrical capacity of such a conductor, increasing its potential by 1 V requires increasing its charge by 1 K. Electric capacity 1 f really big. Thus, the electrical capacity of the Earth is ancient 1/1400 f, Therefore, in practice, it is necessary to use units to create fractions of a farad: millionth fraction of a farad - microfarad (IFF) and a millionth of a microfarad - a picofarad (PF):

1 f = 10 6 μF 1 μF = 10 -6 f 1 pf = 10 -12 f

1 f = 10 12 pf 1 μf = 10 6 pf 1 pf = 10 -6 μf.

Zavdannya 20. There are two positive charges of the body, the first is electricity. 10 pf that charge 10 -8 to, another - electrical capacity 20 pf that charge 2*10 -9 to. What will happen if this body is connected by a conductor? Find out the residual distribution of charges between the bodies.

connection. First body potential Potential of another body So since φ 1 >φ 2, then the charges move from a body with a higher potential to a body with a lower potential.