Ohm's law

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Ohm's law refers to the electric current Follow this conductor Bipartite Voltage Is proportional to the resistance Inversely. This law was developed by German physicists Georg Simon Ohm It was put forward in the paper "Determination of Metal Conductivity Law" published in April 1826. Kollausch uses Dellmann electrometer Studied Ohm's Law in 1849^{[11 ]} 。

The current is measured by the ammeter and the potential difference is measured by the quadrant potentiometer. According to the measurement results, the current strength of the conductor is proportional to the potential difference^{[10 ]} 。

With the development of circuit research, people gradually realize that Ohms The importance of Ohm's law has greatly improved his reputation. In memory of the ohm pair electromagnetics The physics community named the unit of resistance as Ohms , with symbol Ω express.

Chinese name: Ohm's law
Foreign name: ohm's law
Alias: European law
expression: I=U/R

Presenter: Georg Simon Ohm
Proposed time: April 1826
Applicable fields: Physics/Electricity
Applied discipline: physics

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seven application area
eight Law influence

Law definition

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Common description: in the same circuit, the current passing through a conductor is proportional to the voltage at both ends of the conductor and inversely proportional to the resistance of the conductor, which is Ohm's law.

Standard:

(Deformation formula:

;

）

Unit of physical quantity in the formula: I: current, unit: ampere （A）。 U: Voltage in Volts （V）。 R: Resistance in Ohms （ Ω ）。

Circuit formula

Some circuit formulas:

， or

(From the derivation of Ohm's law【

；

】①: voltage is the current and resistance Product of; ②: The resistance is the ratio of voltage to current. Therefore, these deformation formulas are only for calculation reference and have no specific practical significance. )

When Ohm's law is established, the voltage at both ends of the conductor is taken as the abscissa, and the current I in the conductor is taken as the ordinate. The curve drawn is called Volt ampere characteristic curve 。 This is a straight line passing through the origin of the coordinate, its Slope Is the reciprocal of the resistance. Electrical components with this property are called Linear element The resistance is called linear resistance or ohmic resistance.

Figure 1

When Ohm's law does not hold, the volt ampere characteristic curve is not a straight line across the origin, but a curve of different shapes. Electrical components with this property are called Nonlinear element 。

Full circuit formula:

E is power supply emf In Volts（ 5) ; R is Load resistance , r is Internal resistance of power supply ，

The unit is ohm, and the symbol is Ω; The unit of I is ampere (A)

Interpretation of James Maxwell

James Clerk Maxwell The interpretation of Ohm's law is that the electromotive force of a conductor in a certain state is proportional to the generated current. Therefore, the ratio of electromotive force to current, that is, resistance, does not change with current. Here, the electromotive force is the voltage at both ends of the conductor. Referring to the context of this quote, the modifier "in a certain state" is interpreted as being in a normal temperature state, because the resistivity Usually temperature dependent. according to Joule's law , conductive Joule heating (Joule heating) is related to current Conductor The temperature of the conductor will change. Resistance to temperature Dependence In a typical experiment, the resistance depends on the current, so it is difficult to directly check this form of Ohm's law.

Verification of Ohm's Law^{[12 ]}

B is a battery, R is an adjustable resistor, and a tangent galvanometer is connected with a resistor.^{[12 ]} The end point C is connected with a paraffin switch K and one pair of quadrants of the electrometer; Point D is grounded to another pair of quadrants of the electrometer.^{[12 ]} The current flowing through the conductor CD will be measured by the tangent galvanometer, and the potential difference of CD is proportional to the deflection angle of the quadrant electrometer.^{[12 ]} The current is measured by the ammeter and the potential difference is measured by the quadrant potentiometer. According to the measurement results, the current strength of the conductor is proportional to the potential difference^{[10 ]} 。

Circuit diagram to verify Ohm's law^{[12 ]}

Quadrant electrometer^[13] : A light double leaf aluminum blade is suspended in the center of the quadrant shaped box, and the relative quadrant has the same potential.^[13] The blade is connected to a light rod on which a small mirror is hung by a small quartz fiber on the torsion balance head.^[13] There is a brass shell with an opening on the opposite side of the mirror, which forms this device.^[13] Quadrant electrometer can be used to compare the electromotive force of two batteries; Verify Ohm's law; Measure high resistance; Compare the large capacitance with the small capacitance and determine the dielectric constant.^[13] This is achieved by deflecting the aluminum blade by the potential difference of a pair of quadrants.^[13] The deflection angle is measured by shining the lamp on the mirror, which can reflect the light to the scale beyond a certain distance.^[13]

Quadrant electrometer^[13]

Development History

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Ohm The first stage of the experiment is to explore the current generation Electromagnetic force Of attenuation The result of the relationship between the length of the conductor and the length of the conductor was published in his first scientific paper in May 1825. In this experiment, he encountered the measurement electric current The difficulty of strength. Inspired by the galvanometer invented by German scientist Schweig, he Oster about Current magnetic effect Discovery and Coulomb torsion balance Methods A current torsion balance was designed to measure the current intensity. Ohm is generated from the preliminary experiment, and the electromagnetic force of current is related to the length of conductor. There is no direct connection between its formula and today's expression of Ohm's Law. Ohm did not connect the three quantities of potential difference (or electromotive force), current intensity and resistance at that time.

Before Ohm, although there was no concept of resistance, someone had studied the conductivity of metals. In May 1825, Ohm published in his first scientific paper the relationship between the attenuation of the electromagnetic force generated by the current and the length of the wire, which is a paper about the Gavani circuit, but the formula is wrong. In July 1825, Ohm also studied the relative conductivity of metals with the device used in the above preliminary experiment. He measured the wires made of various metals with the same diameter, and determined gold 、 silver 、 zinc 、 brass 、 iron The relative conductivity of metals. Although the experiment was rough and there were many mistakes, Ohm thought that the fact that the current in the whole wire was constant showed that the current intensity could be an important basic quantity of the circuit. He decided to study it as a main observation in the next experiment.

In previous experiments, Ohm used a voltaic stack as the battery pack. The unstable electromotive force of this stack made him have a headache. Later, it was suggested to use bismuth copper thermoelectric couple as the power supply to ensure the stability of the power supply electromotive force.

Ohm experiment and improvement device (3 sheets)

In 1826, Ohm derived his law with an experimental device. The wooden pedestal is equipped with a current torque scale. DD 'is the glass cover of the torque scale, CC' is the dial, s is the magnifying glass for observation, m and m 'are mercury cups, abb' a 'is a bismuth frame, and one leg of the bismuth and copper frames contacts each other, thus forming a thermocouple. A. B is used to generate temperature difference tin Container. In the experiment, the conductor to be studied was inserted into two mercury cups, m and m ', and m and m' became Thermoelectric cell The two poles of.

Ohm prepared conductors with the same cross section but different lengths, connected each conductor to the circuit in turn for experiments, observed the magnitude of the deflection angle of the magnetic needle pulled by the torque, and then changed the conditions for repeated operations. According to the experimental data, the following relations were summarized:

X=q/(b+l) In the formula, x represents the current flowing through the wire, which is proportional to the current intensity. A and B are the two parameters of the circuit, and L represents the length of the experimental wire.

Ohm's paper and draft (7 sheets)

In April 1826, Ohm obtained the famous Ohm's Law, which was rewritten as: X=KSA/L, s is the cross-sectional area of the conductor, K is the conductivity, A is the potential difference between the two ends of the conductor, L is the length of the conductor, and X is the current intensity passing through L. If the resistance l '=L/KS is substituted into the above equation, X=A/I' is the quantitative expression of Ohm's law, that is, the current intensity in the circuit is proportional to the potential difference and inversely proportional to the resistance. In 1827, he published his most famous work Die galvanische Kette^[4] ）》The formula is listed in the article, which clearly points out that the current in the Gavani circuit is proportional to the total voltage and inversely proportional to the total resistance of the circuit. In the formula, S is the current intensity in the conductor (I), A is the voltage at both ends of the conductor (U), and L is the resistance of the conductor (R). It can be seen that this is today's Ohm's law formula for some circuits. In order to commemorate the contribution of ohm to electromagnetism, the unit of resistance is named ohm in the physics world, which is represented by the symbol Ω. 1 ohm is defined as the resistance to a current of exactly 1 ampere at a potential difference of 1 volt.

In 1876, James Clerk Maxwell With colleagues, we have jointly designed several experimental methods to test Ohm's Law, which can highlight the effect of conductors on heat effect Response from.^[1]

experimental verification

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Ohm's first experiment was to explore the relationship between the attenuation of the electromagnetic force generated by the current and the length of the wire. The results were published in his first scientific paper in May 1825. In this experiment, he encountered the difficulty of measuring the intensity of the current. Inspired by the galvanometer invented by German scientist Schweig Current magnetic effect Discovery and Coulomb torsion balance The method is ingeniously combined to design a current torsion scale, which is used to measure the current intensity. Ohm is generated from the preliminary experiment, and the electromagnetic force of current is related to the length of conductor. There is no direct connection between its formula and today's expression of Ohm's Law. Ohm did not change the potential difference (or emf ）, current intensity and resistance.

Before Ohm, although there was no concept of resistance, there were people who had

Conductivity (conductivity). Ohm worked hard. In July 1825, Ohm also used the device used in the above preliminary experiment to study the relative conductivity of metals. He made various metals into wires with the same diameter for measurement, and determined the relative conductivity of gold, silver, zinc, brass, iron and other metals. Although the experiment was rough and there were many mistakes, Ohm thought that the fact that the current in the whole wire was constant showed that the current intensity could be an important basic quantity of the circuit. He decided to study it as a main observation in the next experiment.

In previous experiments, Ohm used a battery pack that Voltaic stack The unstable electromotive force of this stack made him have a headache. Later, it was suggested to use bismuth copper thermoelectric couple as the power supply to ensure the stability of the power supply electromotive force.

In 1826, Ohm derived his law using the experimental device shown in Figure 6 above. The wooden pedestal is equipped with a current torque scale. DD 'is the glass cover of the torque scale, CC' is the dial, s is the magnifying glass for observation, m and m 'are mercury cups, abb' a 'is a bismuth frame, and one leg of the bismuth and copper frames contacts each other, thus forming a thermocouple. A. B is two tin containers used to generate temperature difference. In the experiment, the conductor to be studied was inserted into two mercury cups, m and m ', which became the two poles of the thermoelectric cell.

Figure 7

Ohm prepared conductors with the same cross section but different lengths. Connect each conductor to the circuit in turn for experiment, and observe the torque to pull the magnetic needle Deflection angle And then change the conditions to operate repeatedly. According to the experimental data, the relationship is summarized as follows:

In April 1826, Ohm published a paper, rewriting Ohm's law as: x=ksa/ls is the cross-sectional area of the conductor, K is the conductivity, A is the potential difference between the two ends of the conductor, L is the length of the conductor, and X is the current intensity passing through L. If the resistance l '=l/ks is substituted into the above equation, X=a/I' is the quantitative expression of Ohm's law, that is, the current intensity in the circuit is proportional to the potential difference and inversely proportional to the resistance.

Scope of application

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Ohm's law only applies to Pure resistance circuit , metal conductive and electrolyte Conduction, when conducting gas and Semiconductor element Isometric Ohm's law will not apply.

Micro explanation of the theorem

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A section of metal conductor is provided, Cross sectional area It is S and L in length. When the voltage U is applied to both ends of the conductor field strength E=U/L. At this time, a free electron moves directionally under the action of the electric force F=eE. If the mass of the electron is m, the acceleration of directional movement is a=F/m=eE/m=U (e/mL).

Moving free electrons frequently collide with metal positive ions, which destroys their directional movement and limits the increase of movement speed. After the collision, free electrons have equal opportunities to eject in all directions, losing the characteristics of directional movement before, and have to start again with a directional acceleration with an initial velocity of 0.

The interval between two successive collisions of free electrons is long or short. If the average time is t, then the directional movement rate of free electrons before the next collision vt (subscript t)=at, then the average rate in time t v=at/2. Combined with the previously introduced a=U (e/mL), the average free electron movement rate is v=U (et/2mL).

Substituting the microscopic expression I=neSv of current, I=U (ne two St/2mL)

For certain metal materials, t is a certain value (10 -14 ~10s), that is, for a section of metal conductor, ne two St/2mL is a constant.

Therefore, the Current intensity I is proportional to the voltage U at both ends. The ratio of the voltage at both ends of the conductor to the current intensity in the conductor (2mL/ne two St) is the resistance of this conductor. It can be seen that the resistance of a conductor is proportional to its length, inversely proportional to its cross-sectional area, and proportional to 1/ne ^ 2t. 1/ne two T is determined by the characteristics of the conductor. Therefore, at a certain temperature, the resistance of the conductor is R=ρ L/S. ρ is the resistivity of the conductor. For conductors with the same temperature, resistivity certain.

Limiting causes

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In case of normal temperature or temperature not too low Electronic conduction Of conductor (such as metal), Ohm's law is very accurate Laws 。 When the temperature is low to a certain temperature, the metal conductor may enter from the normal state Superconductive state 。 The resistance of conductor in superconducting state disappears, and there can be current without voltage. In this case, Ohm's law is no longer applicable.

When the temperature or temperature change range is not too large, such as electrolyte (aqueous solution of acid, alkali and salt) Ionic conduction Ohm's law also applies to the conductor of. For gases ionization Under these conditions, Ohm's law does not hold true for the conductive state and some conductive devices, such as electronic tubes and transistors.

application area

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Electrical Engineering and Electronic Engineering

stay electrical engineering and Electronic Engineering Ohm's law is of infinite use because it can express the relationship between voltage and current at the macro level, that is, the relationship between the voltage at both ends of a circuit element and the current passing through it.

physics

In physics, Ohm's law, which will be used in the research on the electrical properties of substances at the micro level, is expressed as

，

A uniform cross-section conductor (e.g., a wire) in a uniform external electric field.

At any two points g and h in the conductor, the voltage is defined as moving the unit charge from point g to point h, Electric field force What needs to be done Mechanical work ：

Among them, Vgh Is the voltage, w yes Mechanical work ， q yes Charge quantity DL is a tiny line element.

Suppose, along the integration path, current density J=jI is uniform current density , and parallel to the tiny line element:

dL=dlI； Where I is Integral path The unit vector of.

Then, the voltage can be obtained:

Vgh = J ρ l ； Among them, l Is the path length of the integration path.

It is assumed that the conductor has uniform resistivity , the current density passing through the conductor is also uniform:

J = I / a ； (The boldface part is vector (Taiwan is called vector ）Among them, a Is the cross-sectional area of the conductor.

Voltage Vgh Abbreviated as V 。 The voltage is proportional to the current:

V = Vgh = I ρ l / a 。 In summary, the relationship between resistance and resistivity is

R = ρ l / a 。 hypothesis J >0, then V > 0 ； The mechanical work to be done by the electric field force when the unit charge is moved from point g to point h w > 0 。 Therefore, the potential of point g is higher than that of point h Potential difference by V 。 From point g to point h, the voltage drop is V ； From point h to point g, the voltage rise is V 。

Give a perfect lattice The movement of electrons in this crystal is equivalent to the movement of electrons in free space Of has Effective quality (effective mass). So, suppose Thermal movement If it is small enough and the periodic structure has no deviation, the resistance of the crystal is equal to zero. However, real crystals are not perfect and often appear Crystal defect (crystal graphic defect), some Lattice point Of atom It may not exist and may be invaded by impurities. So, lattice The periodicity of Disturbance , so electrons will occur scattering 。 In addition, it is assumed that the temperature is greater than Absolute temperature , the atoms at the lattice point will have thermal vibration, and there will be particles with thermal vibration, namely phonon , moving on the crystal. The higher the temperature, the more phonons. Phonons collide with electrons, which is called lattice scattering. Mainly due to the above two kinds of scattering, free electron The flow of will be blocked, so the crystal has limited resistance.

Condensed matter physics

Condensed matter physics To study the properties of matter, especially its electronic structure. stay Condensed matter In physics, the more complex and generalized equations of Ohm's Law are very important, belonging to Constitutive equation (constructive equation) and Transport coefficient theory (theory of transport benefits).

Law influence

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The discovery of Ohm's law and its formula has brought great convenience to electrical calculation. This is a milestone contribution in the history of electricity. Ohm died in 1854. Ten years later British Association for the Advancement of Science In memory of him, the unit of resistance is ohm, referred to as "ohm", and the symbol is Ω , which is the measurement unit of resistance value International System of Units The middle is a unit derived from the current.

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