The internal resistance of the current source. Resistance formula

The electric current in the conductor there is an electric field that forces free charged particles to come into directed movement. The creation of the current particle – a serious problem. To build a device which will maintain the potential difference of the field for a long time in a state – a task which proved the power of humanity only at the end of the eighteenth century.

First attempt

The First attempts to “save electricity” for further research and use was made in Holland. German Ewald jürgen von Kleist and Dutch Peter van Mussenbrock who conducted their research in the town of Leiden, created the world's first capacitor, later called "Leyden jar".

The Accumulation of electric charge has passed under the action of mechanical friction. To use a discharge through a conductor, it was possible for some, relatively short, time period.

The Victory of reason over such ephemeral substance as electricity, turned out to be revolutionary.

Unfortunately, a discharge (an electric current generated by the condenser) lasted so short that to create a constant current could not. Furthermore, the voltage given by the capacitor gradually decreases, which leaves no possibility to obtain continuous current.

I had to find another way.

First source

The experiments of the Italian Galvani for the study of "animal electricity" was the original attempt to find a natural power source in nature. Hanging legs of dissected frogs on metal hooks iron bars, he drew attention to the characteristic reaction of nerve endings.

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However, the findings of Galvani refuted by another Italian, Alessandro Volta. Intrigued by the possibility of obtaining electricity from the animals, he conducted a series of experiments with frogs. But it was the complete opposite of the previous hypotheses.

Volta noticed that the living organism is only an indicator of electrical discharge. When current passes through the muscles of the legs are reduced, indicating potential difference. A source of electric field was the contact of dissimilar metals. The farther apart they are in a number of chemical elements, the greater the effect.

Plates of dissimilar metals laid paper disks impregnated with electrolyte solution, creating a long time is required potential difference. And even if it was low (1.1 V), but the electric current it was possible to explore for a long time. Importantly, the voltage remained unchanged as long.

What's happening

Why in the sources, called “cell” is called this effect?

Two metal electrodes placed in a dielectric have different roles. One supplies the electrons, the other takes them. The process of redox reactions leads to excess of electrons at one electrode, which is called the negative pole, and the lack of the second integer as the positive pole of the source.

In the most simple galvanic cells for oxidative reactions occur at one electrode, recovery – on the other. The electrons arrive at the electrodes from the external part of the circuit. The electrolyte is a conductor of ions inside the source. The resistance force manages the duration of the process.

Copper-zinc element

The Principle of operation of electrochemical cells it is interesting to consider the example of copper-zinc galvanic cell, which is the energy of zinc and copper sulfate. This source plate of copper placed in a solution of sulphate of copper, and a zinc electrode immersed in a solution of sulphate of zinc. Solutions separated by a porous spacer to prevent mixing, but not necessarily touching.

If the circuit is closed, the surface layer of zinc is oxidized. In the process of interaction with liquid zinc atoms into ions appear in the solution. On the electrode releases electrons which can participate in the formation of the current.

Getting on the copper electrode, the electrons participate in the reduction reaction. From the solution on the surface layer do the copper ions in the recovery process, they are converted into copper atoms precipitated on the copper plate.

To Sum up what is happening: the process of working of a galvanic cell is accompanied by the transfer of electrons from reductant to oxidant in the external part of the circuit. The reactions proceed at both electrodes. Inside source, the ion current flows.

Complexity

In principle, any of the possible redox reactions can be used in batteries. But substances that are able to work in a technically valuable items, not so much. Moreover, many reactions require the cost of expensive substances.

Modern batteries have a more simple structure. Two electrodes are placed in a single electrolyte that fills the vessel – a battery case. These design features simplify the structure and reduce the cost of batteries.

Every cell is able to create a constant current.

Resistance to the current allows all ions to be on the electrodes, so the item is running long enough. Chemical reactions, ion formation, sooner or later, cease, the item is discharged.

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

A Bit of resistance

The Use of electric current, no doubt, brought technological progress to a new stage, gave it a giant push. But the power of resistance to the flow of current gets in the way of such development.

On the one hand, the electric current has valuable properties that are used in everyday life and technology, on the other – there is a significant reaction. Physics as a science about the nature tries to establish balance, to align these circumstances.

Resistance to the current caused by the interaction of electrically charged particles with matter, by which they move. To avoid this process in normal temperature conditions it is impossible.

Resistance

The Internal resistance of the current source and resistance of the external part of the chain have a slightly different nature but the same in these processes is to commit the work to move a charge.

The work Itself depends only on the properties of the source and its content: quality of the electrodes and electrolyte, as well as for the external parts of the circuit, the resistance of which depends on the geometrical parameters and chemical characteristics of the material. For example, resistance of metal wire increases with its length and decreases with the extension of the cross-sectional area. When solving a problem, how to reduce resistance, physics recommends the use of special materials.

Current

In accordance with the law of Joule in the conductors is allocated a quantity of heat proportional to the resistance. If the amount of heat to denote the Q_EXT., the current I, duration t, we get:

• Q_EXT. = I^{2 ·} R · t,

Where r-the internal resistance of the current source.

In the whole chain including both internal and external parts of it, will be given the full amount of heat, the formula of which is:

• Q_A = I^{2 ·} R · t + I^{2 ·} R · t = I^{2 ·} (r +r) ·t,

It is Known, as indicated by resistance in physics: an external circuit (all elements except the source) has a resistance R.

Law of the Ohm for a complete chain

Take into Account that most of the work making third-party power within the power source. Its value is equal to the product of the charge carried by the field, and an electromotive force source:

• Q · E = I² · (r + r) · t.

Realizing that the charge is equal to the product of the current intensity at the time of its occurrence, we have:

• E = I · (r + R).

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

• I = E : (r + R).

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

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

The Bit capacity of the source

The main characteristics of the sources can be attributed to the discharge capacity. The maximum amount of electricity that is received when operating in certain conditions, depends on the strength of the discharge current.

Ideally, when you perform certain approximation, the discharge capacity can be considered constant.

For example, a standard battery of potential difference of 1.5 V has a bit capacity of 0.5 A·h If the discharge current is 100 mA, then working for 5 hours.

Charging batteries

The operation of the batteries leads to their discharge. The recovery of batteries, charging small items is carried out using the current, the value of which does not exceed one tenth of the capacity of the source.

The following methods of charging:

• The use of a constant current for a predetermined time (about 16 hours with a current of 0.1 of battery capacity);
• Charging current decreasing to a predetermined value of potential difference;
• The use of asymmetrical currents;
• Consistent application of brief pulses of charging and discharging, in which the first exceeds the second.

Practical work

Sets a task: to determine the internal resistance of the current source and voltage.

To implement it you must be a current source, ammeter, voltmeter, sliding rheostat, a key, a set of conductors.

Using Ohm's law for closed circuit will determine the internal resistance of the current source. For this you need to know the EMF, the resistance value of the resistor.

Calculation formula of the resistance of the current in the external circuit part can be determined from Ohm's law for subcircuit:

• I = U : R

Where I – the strength of the current in the external part of a circuit, is measured by the ammeter; U-voltage on the external resistance.

To improve the accuracy of the measurements are made at least 5 times. What does it do? Measured in the experiment, voltage, resistance, current (or rather, current) are used on.

To determineThe EMF current source, we use the fact that the voltage at its terminals when the open key is practically equal to the EMF.

Collect a chain of series-connected battery, rheostat, ammeter, key. To the terminals of the current source connected to the voltmeter. Razumkov key, remove the statement.

The Internal resistance formula is derived from Ohm's law for the complete chain, we define mathematical calculations:

• I = E : (r + R).
• R = E : I-U : I.

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

The Practical function of batteries are widely used. The undisputed environmental safety of motor no doubt, but to create a succinct, ergonomic battery – the problem of modern physics. Her decision will lead to a new round of development of the automotive equipment.

Compact, lightweight, high-capacity rechargeable batteries are also urgently required in mobile electronic devices. The amount of energy used in them is directly linked to the performance of the device.