Electrical resistance and electrical conductivity. Great encyclopedia of oil and gas

Presentation on the topic "Calculation of conductor resistance" in physics in powerpoint format. The purpose of this presentation for 8th grade schoolchildren is to teach students to measure the resistance of conductors, to establish the dependence of the resistance of a conductor on its length, cross-sectional area and the substance from which it is made. Author of the presentation: Nakhusheva Marita Mukhamedovna, physics teacher.

Fragments from the presentation

Science begins as soon as they begin to measure. Exact science unthinkable without measure. D.I.Mendeleev

Methods for measuring conductor resistance

Avommeter.
Voltmeter and ammeter method

Task 1. Dependence of conductor resistance on length.

We assemble circuit 3, connect the nichrome wire (terminals 1, 2) to a current source and an ammeter. By changing the length of the conductor, observe the change in current strength.

Conclusion 1.

When reducing length nichrome wire The current increases, and as the length increases, the current decreases.
Therefore: for L ↓ ~ I ~ R↓ R ~ L

Task 2. Dependence of conductor resistance on cross-sectional area.

We assemble circuit 3, first connect one nichrome wire (terminals 1, 2) to a current source and an ammeter, then connect two nichrome wires (terminals 1-3, 2-4) to a current source and an ammeter. Observe the change in current strength.

Conclusion 2.

When the cross-sectional area of the nichrome wire decreases, the current strength decreases; when the cross-sectional area increases, the current strength increases.
Therefore: when S ↓ ~ I ↓ ~ R R ~ 1/S

Task 3. Dependence of conductor resistance on the type of substance.

We assemble circuit 3, first connect the nichrome wire (terminals 1, 2) to a current source and an ammeter, then steel wire(terminals 5, 6) connect to a current source and an ammeter. Observe the change in current strength.

Conclusion 3.

The current strength when connecting nichrome wire is greater than when connecting steel (iron) wire.
Using the table, we compare the resistivities of these substances.
Therefore: if I ~ R↓ ~ ρ↓ R ~ ρ

conclusions

Resistance depends on the length of the conductor; the longer the conductor, the greater its resistance.
The resistance of a conductor depends on the cross-sectional area: than smaller area conductor cross-section, the greater the resistance.
The resistance of a conductor depends on the type of substance (material) from which it is made.
The dependence of resistance on the geometric dimensions of the conductor (length and cross-sectional area) and the substance from which it is made was first established by Georg Ohm.
This expression allows you to calculate the conductor length, cross-section and resistivity of the conductor.

Serial connection

At serial connection three conductors, the resistance increases as the length of the conductor increases (R ~ L, L ~ R).

Parallel connection

At parallel connection The cross-sectional area of the conductor increases, the resistance will decrease (at S ↓ ~ R).

Task

Task. Determine the resistance of the telegraph wire between Yuzhno-Sakhalinsk and Tomari if the distance between the cities is 180 km and the wires are made of iron wire with a cross-sectional area of 12 mm2
Task. Calculate the resistance of a copper contact wire suspended to power a tram motor if the length of the wire is 5 km and the cross-sectional area is 0.65 cm2.
Task. What length should I take? copper wire cross-sectional area 0.5 mm2 so that its resistance is equal to 34 Ohms?
Task. Calculate the resistance of a nichrome conductor with a length of 5 m and a cross-sectional area of 0.75 mm2.

Page 1

Addiction electrical resistance conductors from their geometric dimensions is that as the length of the conductor increases and the cross-sectional area decreases, the resistance increases.

Temperature-sensitive converters are based on the dependence of the electrical resistance of a conductor (or semiconductor) on temperature.

Resistance thermometers use the dependence of the electrical resistance of conductors on temperature. Platinum and copper resistance thermometers have been standardized.

Temperature-sensitive converters are based on the dependence of the electrical resistance of a conductor (or semiconductor) on temperature.

Their action is based on the dependence of the electrical resistance of conductors on temperature. Graphs of their resistance versus temperature are shown in Fig. 2.16. In practice, these are straight lines. The TKES value of copper is higher than that of platinum, therefore TCM is more sensitive to temperature changes, which explains the greater steepness of the graph. However, the upper temperature limit of measurement for TSM is 200 C, and for TSP - plus 1100 C. The lower limits are, respectively, minus 200 and minus 260 C.

The principle of operation of the converters is based on the dependence of the electrical resistance of conductors or semiconductors on temperature.

The operating principle of the converters is based on the dependence of the electrical resistance of conductors or semiconductors on temperature.

Technical characteristics of indicating pressure thermometers.

The operation of these thermometers is based on the dependence of the electrical resistance of a conductor (thin wire) on temperature. A resistance thermometer consists of a winding made of thin wire on a special frame made of insulating material. The sensing element is enclosed in a protective sleeve.

Thermal resistance sensors are based on the dependence of the electrical resistance of conductors on temperature. There are two ways to use RTDs as sensors. In the first method, the temperature of the thermal resistance is determined by the temperature environment, since the current flowing through the thermal resistance thread is selected small enough so that the heat generated by it does not affect the temperature of the thermal resistance. This method is used in temperature sensors.

Thermal resistance sensors are based on the dependence of the electrical resistance of conductors on temperature. There are two ways to use thermal resistance sensors. In the first method, the temperature of the thermal resistance is determined by the ambient temperature, since the current flowing through the thermal resistance is selected small enough so that the heat it generates does not affect the temperature of the thermal resistance. This method is used in temperature sensors.

Strain-sensitive (wire) transducers are based on the dependence of the electrical resistance of the conductor on the mechanical stress caused in it.

To exist in the explorer direct current, that is, the movement of electrons with constant speed it is necessary that an external force ($F$) acts continuously, equal to:

where $q_e$ is the electron charge. Therefore, electrons in a conductor move with friction. Or else they say that conductors have electrical resistance (R). Electrical resistance is different for different conductors and may depend on the material from which the conductor is made and on its geometric dimensions.

Ohm's law can be used to measure resistance. To do this, measure the voltage at the ends of the conductor and the current flowing through the conductor, use Ohm's law for a homogeneous conductor, and calculate the resistance:

Dependence of resistance on geometric dimensions and conductor material

If we carry out a series of experiments to measure the resistance of a homogeneous conductor of constant cross-section, but different lengths($l$), then it turns out that its electrical resistance is length ($R\sim l$).

We carry out the following experiments for a homogeneous conductor, the same material, the same length, but different cross-sections, then we find that the resistance is inversely proportional to the cross-sectional area ($R\sim \frac(1)(S)$).

And the third experiment, to study the electrical resistance of conductors, is carried out with conductors from different materials, with the same length and cross-section. Result: resistance also depends on the material of the conductor. All the results obtained are expressed by the following formula for calculating resistance:

where $\rho$ is the resistivity of the material.

The resistance of the circuit section between sections 1 and 2 ($R_(12)$) is called the integral:

For a homogeneous (in terms of resistivity) cylindrical conductor ($\rho =const,S=const\ $) the resistance is calculated using formula (3).

The basic SI unit of resistance is the Ohm. $1Ohm=\frac(1V)(1A).$

Resistivity

The resistivity of a material is equal to that of a particular substance, 1 m high and with a cross-sectional area of $1 m^2$.

In SI, the basic unit of resistivity is $Ω\cdot m$.

The resistivity of substances depends on temperature. For conductors, this dependence can be approximately expressed by the formula:

where $(\rho )_0$ is the resistivity of the conductor at a temperature of 00C, $t$ in degrees Celsius, $\alpha $ is the temperature coefficient of resistance. For large quantity metals at temperatures in the range $0(\rm()^\circ\!C)\le t\le 100(\rm()^\circ\!C),$ $3.3\cdot (10)^(-3 )\le \alpha \le 6.2\cdot (10)^(-3)\frac(1)(K)$.

Temperature coefficient of resistance of this substance defined as:

$\alpha $ gives a relative increase in resistance with an increase in temperature by one degree. That is, based on (6), we obtain a nonlinear dependence of resistivity on temperature, but $\alpha $ does not change as much with increasing (decreasing) temperature, and this nonlinearity is not taken into account in most cases. For metals $\alpha >0,\ $for $\alpha

The dependence of resistivity on temperature is explained by the dependence of the average free path of a charge carrier on temperature. This property is used in various types measuring instruments And automatic devices.

Specific electrical conductivity of a substance

The reciprocal of resistivity is called electrical conductivity ($\sigma$):

In the SI system, the basic unit of electrical conductivity is 1 $\frac(Siemens)(m)$ ($\frac(S)(m)$). The value $\sigma $ characterizes the ability of a substance to conduct electricity. Electrical conductivity depends on the chemical nature of the substance and the conditions (for example, temperature) under which this substance is located. If we saw from equation (4) that $\rho \sim t$, then, therefore, $\sigma \sim \frac(1)(t).\ $It should be noted that when low temperatures these dependencies are violated. The phenomenon of superconductivity is observed. At $T\to 0,\$ an absolutely pure metal with ideally regular crystal lattice at absolute zero resistivity must be equal to zero, accordingly, the conductivity is infinite.

Example 1

Task: Calculate the resistance of the conductor (R), if at one end it is maintained at a temperature of $t_1$, at the other $t_2$. The temperature gradient along the axis of the conductor is constant. The resistance of this conductor at a temperature of 00C is equal to $R_0$.

Based on the constancy of the temperature gradient along the axis of the conductor, we write that:

\[\frac(dt)(dx)=k\ \left(1.1\right),\]

where $k=const.$ Therefore, we can find the law of temperature change when moving along the conductor, that is, t(x). To do this, we express $dt$, we get:

Let's find the integral of (1.2), we get:

Let's place the origin of coordinates at the point that coincides with the end of the conductor, which has a temperature of $t_1$. Then, using (1.3), we substitute x=0 and find the constant C:

At the other end, the temperature of the conductor is equal to $t_2, let us substitute in (1.3), take into account (1.4) $x=l$, where $l$ is the length of the conductor, we obtain:

To calculate the resistance we use the formula:

where $\rho =(\rho )_0\left(1+\alpha t\right)$. Let's calculate the integral:

Instead of k in expression (1.7), we substitute what we got in (1.5), we have: \

where $(\rho )_m$ is the mass density of the conductor. Let us express the length of the rod from (2.2), we obtain:

We find the cross-sectional area of the conductor in accordance with the formula:

Substituting (2.3) and (2.4) into (2.1) we get:

Answer: $R=\frac(\rho )((\rho )_m)\frac(16m)((\pi )^2d^4).$