Internal resistance of a current source. Resistance - Formula

An electric current in a conductor arises under the influence of an electric field, causing free charged particles to come in directional motion. Creating particle current is a serious problem. To build such a device that will maintain the potential difference of the field for a long time in one state is a task that mankind could only solve by the end of the 18th century.

current resistance formula

First attempts

The first attempts to “accumulate electricity” for its further research and use were made in Holland. The German Ewald Jürgen von Kleist and the Dutchman Peter van Mushenbruck, who conducted their research in the town of Leiden, created the world's first capacitor, later called the "Leiden bank."

The accumulation of electric charge has already passed under the action of mechanical friction. It was possible to use the discharge through the conductor for some rather short period of time.

The victory of the human mind over such an ephemeral substance as electricity turned out to be revolutionary.

Unfortunately, the discharge (the electric current created by the capacitor) lasted so short that it could not create a direct current . In addition, the voltage supplied by the capacitor gradually decreases, which leaves no opportunity to receive a continuous current.

It was necessary to look for a different way.

First source

internal resistance of a current source

Galvani’s Italian experiments on the study of “animal electricity” were an original attempt to find a natural source of current in nature. Hanging the legs of the prepared frogs on the metal hooks of the iron lattice, he drew attention to the characteristic reaction of nerve endings.

However, the conclusions of Galvani were refuted by another Italian - Alessandro Volta. Interested in the possibility of generating electricity from animal organisms, he conducted a series of experiments with frogs. But his conclusion was the exact opposite of the previous hypotheses.

Volta drew attention to the fact that a living organism is only an indicator of an electric discharge. With the passage of current, the muscles of the legs contract, indicating a potential difference. The source of the electric field was the contact of dissimilar metals. The farther apart they are in a series of chemical elements, the greater the effect.

Dispersed metal plates laid with paper disks impregnated with an electrolyte solution created the necessary potential difference for a long time. And although it was low (1.1 V), but the electric current could be investigated for a long time. The main thing is that the tension remained unchanged for as long.

current resistance

What's happening

Why do sources called "galvanic cells" cause such an effect?

Two metal electrodes placed in a dielectric play different roles. One delivers electrons, the other accepts them. The redox reaction leads to the appearance of an excess of electrons on one electrode, which is called the negative pole, and a deficiency on the second, we denote it as the positive pole of the source.

In the simplest galvanic cells, oxidative reactions occur on one electrode, and reduction reactions on another. Electrons come to the electrodes from the outside of the circuit. The electrolyte is a conductor of ion current inside the source. Resistance forces the duration of the process.

Copper-zinc element

It is interesting to consider the principle of operation of galvanic cells by the example of a copper-zinc galvanic cell, whose action is due to the energy of zinc and copper sulfate. In this source, a copper plate is placed in a solution of copper sulfate, and a zinc electrode is immersed in a solution of zinc sulfate. The solutions are separated by a porous pad to avoid mixing, but be sure to touch.

If the chain is closed, the surface layer of zinc is oxidized. In the process of interaction with a liquid, zinc atoms, having turned into ions, appear in solution. Electrons are released on the electrode that can take part in the formation of current.

Getting on a copper electrode, electrons take part in the reduction reaction. Copper ions come from the solution to the surface layer, during the recovery process they turn into copper atoms, deposited on a copper plate.

We summarize what is happening: the process of operation of a galvanic cell is accompanied by a transition of the reducing agent electrons to the oxidizer along the outer part of the circuit. Reactions go on both electrodes. An ion current flows inside the source.

Use difficulties

In principle, any of the possible redox reactions can be used in batteries. But there are not so many substances that can work in valuable technical elements. Moreover, many reactions require expensive substances.

Modern batteries have a simpler structure. Two electrodes placed in one electrolyte fill the vessel - the battery case. Such design features simplify the structure and reduce the cost of batteries.

Any galvanic cell is capable of creating direct current.

resistance force

The current resistance does not allow all ions to be simultaneously on the electrodes, so the cell works for a long time. The chemical reactions of the formation of ions sooner or later cease, the element is discharged.

The internal resistance of the current source is of great importance.

A bit about resistance

The use of electric current, undoubtedly, brought scientific and technological progress to a new stage, gave him a giant impetus. But the force of resistance to the flow of current becomes in the way of such a development.

determine the internal resistance of the current source

On the one hand, electric current has invaluable properties used in everyday life and technology, on the other - there is significant opposition. Physics as a science of nature is trying to establish a balance, bring these circumstances into line.

Current resistance occurs due to the interaction of electrically charged particles with the substance through which they move. It is impossible to exclude this process under normal temperature conditions.

Resistance

The internal resistance of the current source and the reaction of the external part of the circuit are of a slightly different nature, but the same thing in these processes is the work of moving the charge.

The work itself depends only on the properties of the source and its filling: the qualities of the electrodes and electrolyte, as well as for the external parts of the circuit, the resistance of which depends on the geometric parameters and chemical characteristics of the material. For example, the resistance of a metal wire increases with its length and decreases with the expansion of the cross-sectional area. In solving the problem of how to reduce resistance, physics recommends the use of specialized materials.

Work current

In accordance with the Joule-Lenz law, the amount of heat in the conductors is proportional to the resistance. If the amount of heat designate Q int. , current I, its flow time t, then we get:

  • Q int. = I 2 r t

where r is the internal resistance of the current source.

In the whole chain, including both its internal and external parts, the total amount of heat will be released, the formula of which has the form:

  • Q full = I 2 r · t + I 2 R t = I 2 (r + R)

It is known how resistance is denoted in physics: the external circuit (all elements except the source) has resistance R.

Ohm's law for the full chain

Consider that the main work is performed by external forces inside the current source. Its value is equal to the product of the charge transferred by the field and the electromotive force of the source:

  • q · E = I 2 · (r + R) t.

realizing that the charge is equal to the product of the current strength by the time of its flow, we have:

  • E = I · (r + R).

In accordance with causal relationships Ohm's law has the form:

  • I = E: (r + R).

The current strength in a closed circuit is directly proportional to the EMF of the current source and inversely proportional to the total (total) resistance of the circuit.

Based on this regularity, it is possible to determine the internal resistance of the current source.

Source discharge capacity

The main characteristics of the sources include discharge capacity. The maximum amount of electricity obtained during operation under certain conditions depends on the strength of the discharge current.

voltage resistance current

In the ideal case, when certain approximations are performed, the discharge capacity can be considered constant.

For example, a standard battery with a potential difference of 1.5 V has a discharge capacity of 0.5 Ah. If the discharge current is 100 mA, it works for 5 hours.

Battery Charging Methods

Using batteries will drain them. Recovery of batteries, charging of small-sized cells is carried out using current, the value of which does not exceed one tenth of the capacity of the source.

resistance formula

The following charging methods are available:

  • the use of a constant current for a given time (about 16 hours with a current of 0.1 battery capacity);
  • charging with a step-down current to a preset value of the potential difference;
  • use of unbalanced currents;
  • sequential use of short impulses of charging and discharging, in which the time of the first exceeds the time of the second.

Practical work

The task is proposed: to determine the internal resistance of the current source and EMF.

To do this, you need to stock up on a current source, ammeter, voltmeter, slide rheostat, key, set of conductors.

Using Ohm's law for a closed circuit will determine the internal resistance of the current source. To do this, you need to know its EMF, the resistance value of the rheostat.

The calculated formula for the current resistance in the outer part of the circuit can be determined from Ohm's law for the circuit section:

  • I = U: R,

where I is the current strength in the outer part of the circuit, measured by an ammeter; U is the voltage at the external resistance.

To increase accuracy, measurements are made at least 5 times. What is it for? The voltage, resistance, current (or rather, current strength) measured during the experiment are used below.

To determine the EMF of the current source, we use the fact that the voltage at its terminals with an open key is almost equal to the EMF.

Assemble a chain of sequentially connected batteries, rheostat, ammeter, key. We connect a voltmeter to the terminals of the current source. Opening the key, take his testimony.

The internal resistance, the formula of which is obtained from Ohm's law for a complete circuit, is determined by mathematical calculations:

  • I = E: (r + R).
  • r = E: I - U: I.

Measurements show that the internal resistance is much less than the external.

The practical function of rechargeable batteries and batteries is widely used. The indisputable environmental safety of electric motors is beyond doubt, but creating a capacious, ergonomic battery is a problem of modern physics. Its solution will lead to a new round of development of automotive technology.

Small-sized, lightweight, capacious rechargeable batteries are also extremely necessary in mobile electronic devices. The energy reserve used in them is directly related to the performance of the devices.


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