4.2. 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 – The direct method scheme

If voltage drop on the internal resistance of the source Ir<<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U_V is comparable with voltmeter's error or even unknown, then the voltmeter scale reading U_V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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=_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.

5. Data processing

(Same as in Laboratory work № 2-2).

6. Work execution order and experimental data analysis

5.1. 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 R₂, 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 R₂=0, thus .

3. Set the potentiometer slider in the middle. Lock the switches К₁ and then К₂.

4. M

   

   Fig. 19 – The compensation method scheme

   oving the potentiometer slider, obtain absence of current through the microampermeterI=0.

5. Only at the moment of compensation we can write down the voltmeter scale reading _Xi into a measurements table. To disconnect switches К₁ and К₂.

6. To set sequentially values of resistance of one-decade resistors box R₂ equal 10k, 30k, 50k, 70k, thus . It is equivalent to a changing of sources. Make measurements according to points 3, 4 and 5.

7. Calculate average value of EMF <_X> (41), abmodality each measurement _Xi (42), sum of squares of abmodalities (43).

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

9. Calculate absolute device error _X^DEV according (45):

,

where  - accuracy class and U_max – grid limit of voltmeter.

10. Calculate total absolute error  (46) and relative error _ (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.