Resistivity is a physical quantity used to express the resistance characteristics of various substances. The length of a certain material is 1m, and the cross-sectional area is 1mtwoOf conductorsresistance, which is numerically equal to the resistivity of this material.It reflects the property of substances that hinder the current. It is not only related to the type of substances, but also affected bytemperature、pressureandmagnetic fieldAnd other external factors[1]。
Chinese name
resistivity
Foreign name
resistivity
expression
ρ=RS/L
Applicable fields
Mathematical Science
Applied discipline
Physics
Role
Calculation of conductor resistance, etc
influence factor
Material type, temperature, pressure, surrounding magnetic field, etc
Resistivity is used to represent various substancesresistanceThe physical quantity of the characteristic.1m long and 1m cross sectional area made of certain materialtwoOfconductorOfresistance, numerically equal to the resistivity of this material[2]。[10]
ResistivityIt is a physical quantity used to express the resistance characteristics of various substances.When the temperature is constant, the resistance of the material is:[4]
Of which
Is resistivity,
Is the length of the material,
Is the cross-sectional area of the material.It can be seen that the resistance of the material is proportional to the length of the material, that is, the longer the length is, the greater the resistance of the material is when the material and the cross-sectional area are unchanged;It is inversely proportional to the cross sectional area of the material, that is, when the material and length are constant, the greater the cross sectional area, the smaller the resistance[4]。
From the above formula, the definition of resistivity is:[4]
Derived formula:[4]
Note: Deduction formula assumption
Is the material volume and meets
For materials with uneven cross section, it can be regarded as a series of countless uniform cross section materials with extremely short length.At this time, there are:
Note:
Indicates that when the length is
Cross sectional area at
explain
Announce
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1. ResistivityρIt is not only related to the material of conductor, but also to the temperature of conductor.In the range of small temperature change, the resistivity of almost all metals changes linearly with temperature, that isρ=ρzero(1+at）, wheretIs the temperature in Celsius,ρzeroIs the resistivity at 0 ℃,aIt is the temperature coefficient of resistivity, which can be used to make resistance thermometer. The resistivity of some alloys is little affected by temperature, and is often used as standard resistance[5]。
2. Since the resistivity changes with temperature, the physical state of the resistance of some electrical appliances must be described.For example, the resistance of a "220V, 40W" lamp filament is 1210 Ω when it is normally lit, and only about 100 Ω when it is not powered on[5]。
3. Resistivity and resistance are two different concepts. Resistivity is an attribute reflecting the blocking effect of substances on current, and resistance is an attribute reflecting the blocking effect of substances on current[5]。
influence factor
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The resistivity is not only related to the material type, but also to the external factors such as temperature, pressure and magnetic field.When the temperature of metal material is not high,ρAnd temperaturetThe relationship of (℃) isρt=ρzero(1+at）, whereρtAndρzeronamelytResistivity at ℃ and 0 ℃;aIs the temperature coefficient of resistivity, which is related to the material.ManganinaAbout 1 × 10-5/℃ (its value is very small), and the resistance value of the resistor made of it changes very little with temperature in the normal temperature range, which is suitable for standard resistance.Of known materialsρAfter the value changes with temperature, a resistance thermometer can be made to measure the temperature.Semiconductor materialaIt is generally negative and has a large value.The resistance thermometer has high sensitivity.Some metals (such as Nb and Pb) or their compounds, when the temperature drops to several K or more than ten K (absolute temperature),ρThe superconducting material has a wide application prospect.Material utilizingρThe properties that change with magnetic field or stress can be made into magnetoresistance orResistance strain gauge, which are used to measure the magnetic field or the mechanical stress on objects, and are widely used in engineering[6]。
It can be seen that the resistivity of pure metal in conductor is small, while that of alloy is large.The resistivity of silver is the smallest, but silver is expensive. Usually, silver is seldom used as conductor, and it is only used for special needs,wirewayGenerally, they are made of copper or aluminum with low resistivity. Aluminum is cheaper than copper, so aluminum conductors are used a lot.The resistance wire of electric furnace and resistor is generally made of alloy with high resistivity[7]。
The resistivity of all materials changes with temperature, and the resistivity of metal increases with temperature, so the resistance of metal conductor also increases with temperature. This property of resistance can be used to make resistance thermometer;If the change of conductor resistance with temperature is known, then the resistance of conductor can be measured, and the temperature of conductor can be known in turn[7]。
application
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Resistivity reflects conductorConductivityGood or badphysical quantity。Low resistivity and good conductivity;High resistivity and poor conductivity.The size of the resistivity is determined by the nature of the material itself, and the resistivity of the same material changes with the temperature. Generally, the temperature is high and the resistivity is large.The following table lists the resistivity of some common materials at room temperature[8]。
Resistivity of common materials (20 ℃)
It can be seen from the above table that the resistivity of metals and alloys is very small;The resistivity of bakelite and rubber is very high.When in use, appropriate materials can be selected according to the resistivity table as required.For example, in power supply, transmission and distribution lines, in order to reduce resistance, copper, aluminum and other low resistivity materials should be used to make conductors;The insulation part of electrical appliances and electrical tools in use should be selectedBakelite、rubberConductor made of materials with equal high resistivity[8]。
When assembling special conductors for high energy consuming appliances such as air conditioners, copper conductors with small resistivity and large wire diameter are often selected because of their high power and large working current[8]。
The resistivity of various materials varies with temperature.The resistivity of pure metal increases with the increase of temperature. The resistance thermometer is made of this property of metal, which can be used to measure very high temperatures.Precision resistance thermometers are made of platinum.Given the corresponding relationship between the resistance of the platinum wire and the temperature, the ambient temperature can be known by measuring the resistance of the platinum wire.Some alloys, such as manganin and constantan, have almost no effect on the resistivity due to temperature changes, and are often used to make standard resistors[8-9]。
