Measurement of EMF of a source by direct method

During a direct measurement of EMF source (Fig. 18), the potential difference, which shows the voltmeter (64), is smaller than EMF on the value of voltage drop on the internal resistance of the source Ir.

 

Fig. 18 – Thedirect method scheme

If voltage drop on the internal resistance of the source Ir <<D U _V is more smaller than voltmeter's error, then the voltmeter scale reading U _V»e _Х can be taken equal to the value of EMF of the source, and the measurement error has to be taken equal to the voltmeter's error. If the voltage drop inside the source Ir ~D U _V is comparable with voltmeter's error or even unknown, then the voltmeter scale reading U _V ¹ e _Х will not match to real value of the source EMF.

Current in this circuit we define by Ohm’s law for closed circuit (61):

,

where R_V – resistance of voltmeter.

Then voltages drop on voltmeter (64):

. (66)

From (66) we can see, that the voltmeter scale reading U _V ¹ e _Х will be differs from EMF if resistance of the voltmeter R _V~ r_X is comparable with internal resistance of the source. For example, if R _V = r_X, then U _V=e _Х / 2.

Taking into account (66), we obtain relative error of this direct measurement of EMF in percent:

. (67)

Relative error of the direct measurement (67) also depends on a relation R _V / r_X.

Conclusion: For measuring of the EMF of a source by a direct method, at first it is necessary to find a range of values of internal resistances of source at which measuring it is possible to consider correct.

 

 

Data processing

(Same as in Laboratory work № 2-2).

Work execution order and experimental data analysis

Compensation method

1. Mount the scheme Fig. 19. As a modelling source of the EMF we choose a source e₁, which is on the left side of a laboratory board. In series with it we connect one-decade resistors box R ₂, which simulates the sources internal resistance. Auxiliary source e₂ is on the right side of a laboratory board.

2. Turn on both observable and auxiliary sources. Set the value R ₂=0, thus .

3. Set the potentiometer slider in the middle. Lock the switches К ₁ and then К ₂.

4. Moving the potentiometer slider, obtain absence of current through the microampermeter I =0.

5. Only at the moment of compensation we can write down the voltmeter scale reading e_Xi into a measurements table. To disconnect switches К ₁ and К ₂.

6. To set sequentially values of resistance of one-decade resistors box R ₂ equal 10 kW, 30 kW, 50 kW, 70 kW, thus . It is equivalent to a changing of sources. Make measurements according to points 3, 4 and 5.

7. Calculate average value of EMF <e_X> (41), abmodality each measurement De_Xi (42), sum of squares of abmodalities (43).

8. For known the sum of squares of abmodalities calculate statistical absolute error De_X^ST (44) for confidence probability a=0,95, number of measurements n =5 and Sdudent’s coefficient .

9. Calculate absolute device error De_X^DEV according (45):

,

where b - accuracy class and U _max – grid limit of voltmeter.

10. Calculate total absolute error De (46) and relative error d_e (47) of measurements.

11. Write a final result as a confidence interval and relative error (48).

12. Conclude about valuess of statistical and device absolute errors.

5.2. Direct method

1. Mount the scheme Fig. 18. As a modelling source of the EMF we choose a source e₁, which is on the left side of a laboratory board. Resistors box R ₂ simulate the sources internal resistance.

2. Turn on observable source. Set the value R ₂=0, thus . Lock the switche К ₁.

3. Write down the voltmeter scale reading U_i into a measurements table.

4. To set sequentially values of resistance of resistors box R ₂ equal 10 kW, 30 kW, 50 kW, 70 kW, 90 kW, thus . It is equivalent to a changing of sources. Make measurements according to point 3.

5. Calculate a relative error (67) of each direct measurement (for each another sourse).

6. Represent the final result by a draph of dependence error of direct method of measurements β _i ^DIR from relative value of internal resistance of a source r_Xi / R_V .

7. Conclude about range of values of internal resistances of source at which measuring it is possible to consider correct (when the value of error of direct method of measurements b _i ^DIR is less).

Test questions

1. What is potential, voltage (potential difference), EMF of the source, voltage drop?

2. How does Ohm's law look for uniform part of circuit, for non-uniform part of circuit, for the closed circuit?

3. When do potentials difference on the terminals of the source is equal to its EMF?

4. What is compensation method of measurement EMF of sources? Draw the scheme.

5. How the voltage between the points of the circuit can be calculated, if all EMFs of all sources and resistances of all parts of the circuit are known?

6. What is compensated in a compensation method of measuring of the EMF? Draw the scheme.

 

 

Content of the report

 

Homework toLaboratory work №2-3

(Answers on test questions from p.14)

…