A purpose of the work is to measure resistance of a conductor by different methods, to calculate the specific resistance, to examine relation Rp= f(1).
Instrumentation and appliances: an experimental plant.
Theoretical part
1. The ordered motion of electric charges is called the electric current. An electric current in metals is the motion of the conductivity electrons. In conducting solutions (electrolytes) ions are the mobile charges. The ions and the electrons carry charges in gases.
Intensity and density are the quantative characteristics of the electrical current. Intensity of current is the charge dq passesthrough a cross section of a conductor in a time dt:
.
If the same amount of electric charges flows through any section of conductor at the equal period of time, the current intensity is constant value I= dq/dt = const. If the current changes by time, it is alternating current dq/dt≠const. The intensity of current is a scalar value and measured in amperes in the SI system. Current intensity is measured in milliamperes ( mA ) and microamperes ( μA ) too.
If current is assigned irregularly along the surface S, then the current density j is defined in every point of the surface. The current density is the ratio
,
where dS is an area perpendicular to the current direction dI which goes through this area.
The current intensity I through the given surface S can be found with the help of integration:
.
If the current I is assigned regularly through the given surface S then the current density- j=I/S=const. The current density is a vector value and inSI system measured in amperes divided by square meter ( A/m2 ).
The density of a charge j can be assigned by concentration of the charges, its value and velocity
.
2. There is relationship between the voltage U applied to the ends of the conductor and the current in it for each conductor if the condition of the conductor is invariable:
. (8.1)
Its the Ohms law for the part of the electric circuit in integral form. According to the Ohms law in the differential form j=σE the current density j in the conductor is directly proportionate to the electric intensity E in it, where σ is specific electroconductivity of the conductor. The Ohms law for the closed circuit is
,
where ε - electromotive force,
R - external resistance of the conductor,
r - internal resistance of current source.
When the current passes through the conductor, the latter is being heated. The quantity of the produced heat in the conductor is proportionate to its resistance, square value of current intensity and time:
. (8.2)
If the current intensity changes in time, then:
. (8.3)
The formulas (8.2) and (8.3) represent the Joule-Lenz law. The heat quantity Q, which turns from the volume unit into the time unit of the conductor, is called the power of the current. The Joule-Lenz law in differential form is:
.
3. Simple electric circuits are closed loops. The calculation of the ramified electric circuit is more complex but significantly simplified if we use Kirchhoffs laws.
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The first law deals with the junction points and states: the algebraic sum of the currents at any junction point equals to zero (Fig. 8.1). For the junction point A:
or - I 1- I 2+ I 3=0.
The second law deals with electric circuits: for any closed loop the algebraic sum of all incidences of voltage IiRi is equal to the algebraic sum of all the electromotive forces εi in this circuit.
For the 1 circuit
.
Figure 8.1
For the 2 circuit
.
4. The conductors resistance is directly proportional to its length and inversely proportional to its cross-section area
, (8.4)
where ρ - the specific resistance of the conductor,
l - the length of the conductor,
S - cross-section area.
The conductors in the electric field can be connected in series and parallel.
When the conductors connected in series the current has the same value of I (fig. 8.2).
Voltage drop in each resistance
; 
; 
.
Figure 8.2
Adding right and left parts of these equations we obtain:
.
Hence it follows, that for any n amount of resistances connected in series there is a common resistance:
. (8.5)
In case of parallel resistance the common current I is branched into 
currents.
Let us consider parallel connection for three conductors (fig. 8.3):
Figure 8.3
Voltage drop in each resistance is the same:
;
; 
; 
; 
; 
.
In general for n amount of the conductors connected in parallel the total resistance may be expressed by the formula
.
Experimental part
An experimental device to measure the resistance consists of the column with wire and measuring block (fig.8.4).
Figure 8.4
On the column there are two motionless brackets and a traveling one which can move along the column and be fixed in any position. The mark which is drawn between the upper and the lower brackets facilitates to define the length of the segment of resisting wire being measured.
The measuring part is placed in the separate block which has milliamperemeter, voltmeter and operating keys. Milliamperemeter is plugged in the resisting wire circle and used to measure the current and voltmeter to measure the voltage in the measured length of resisting wire. The switch W 1 is used to choose the type of work and the switch W 2 to choose the accuracy of current and voltage measurement.
1. Move the traveling bracket for 0,7 - 0,8 of length of the resisting wire, take it from the basis.
2. Press button W 1 .
3. Press button W3 ̲ʔ.
4. When pressing button W2 the scheme works in the Fig. 8.5.
Figure 8.5
5. Write down the measurements which shows millliamperemeter and voltmeter and calculate R using the formula 
, Ra = 0,15 Om, Ra = 2500 Om.
6. When pressing button W 2, the scheme in the Fig. 8.6 works.
7. Make measurements of the millliamperemeter and voltmeter readings and calculate R using the formula:
, 
.
Figure 8.6
8. Measure with micrometer the diameter of the wire d, the length of the wire from the basis to the traveling contact l, calculate the specific resistance r using the formula
.
9. Using one of the schemes of connection build up the constant value of the current I with the help of regulator. Moving the traveling contact of the resisting wire for a few marks find 8-10 values of the U.
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10. Count 8-10 values of R using the formula which correspond to the switching on scheme.
11. Fill in the table with data:
| Ia, A | |||||||||
| I, m | |||||||||
| U v,V | |||||||||
| Rp, Om |
12. Build up the graph Rp =f(I).
13. Count the error for Rp. Make a conclusion about the work done.
Control questions
1. What is an electric current? Write the formula for the direct current.
2. Write the definition and formula for the alternating current.
3. Write the definition and formula for the current density.
4. Write the relationship between the current intensity and its density.
5. Write the Ohms law in integral form.
6. Write the relationship between the conductor resistance and conductor electroconductivity.
7. Write the Ohms law for the closed circuit.
8. Formulate and write the Joule Lenz law.
9. Formulate and write the first and the second Kirchhoffs laws.
10. Write the dependence of the conductor resistance on its cross-section.
11. Deduce the formula for counting two resistors connected in series and parallel.
This instruction is worked out by S. Lushchin, reader of the physics chair.
Reviewer: S. Loskutov, professor of the physics chair.
22.2
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2. .. . -.: , 1998, . II, 1.1-1.14.
3. .., .. . -.: , 1972, . II, 1.4-1.8.
4. .., .. . -: , 1989. 13.1-13.5
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LABORATORY WORK 23
