Laboratory work № 2-3 implementation protocol

1) Topic: DETERMINATION OF EMF OF CURRENT SOURCE.

2) Goal: Studying EMF measurement methods: a) compensation method; b) method of direct measurements.

3) Scheme of laboratory research facility:

a) compensation method	b)direct measurements

4) Table of measuring instruments:

№	Name	Type	Serial number	Grid limit	Grid unit	Accuracy class
1.	One-decade resistors box R2
2.	Voltmeter
4.	Microampermeter (zero-indicator)

5) Equations for calculation:

5.1) Compensation method:

U_V = IR_V = ε_x –Ir, when I =0 (compensation condition), then U_V = ε_x.

Hhere r = r_x + R₂.

Statistical absolute error of measurements we estimate by Sdudent’s equation (27):

,

where a =0,95 – confidence probability; n=5 – number of measurements;

t _{0,95; 5}= 2,77 – Sdudent’s coefficient.

Device error of voltmeter (28):

,

where β_V - is the accuracy class of voltmeter, e _max - its grid limit of voltmeter.

Total absolute error (29):

.

Relative error of measurements incompensation method:

.

5.2) Direct measurement method:

U_V = IR_V = ε_x –Ir, where r = r_x + R₂.

We don’t calculate an absolute error of direct measurement method because we represent the final result by a draph.

Relative error of direct measurement method:

,

where < e _x> – average value of EMF from point 5.1).

6) Table of measurements: RV=2×10^5 W, r1= 2 k W.
Compensation method	Direct measurement method
	№	r, kΩ	e x, V	De xi, V	(DeI) ^2, V^2	U, V	β i^DIR, %	r / RV
	1	rх + 0
	2	rх + 10
	3	rх + 30
	4	rх + 50
	5	rх + 70
	6	rх + 90	–	–	–
	Average evalue <ex>=	…		…

7) Calculation of quantities:

7.1) Compensation method:

Statistical absolute error:

.

Device error of voltmeter:

.

Total absolute error and relative error of incompensation method:

; .

7.2) Direct measurement method:

Relative error of direct measurement method:

; ;

; ;

; .

 

8) Final results: 8.1) Compensation method: ex = (< e x> ± De x) a V = (... ±...)0,95 V; = … %. 8.1) Direct measurement method: Graph of dependence of β2^DIR from r/RV :

9) Conclusions: Incompensation method … (ststistical or device) error make a main contribution to an absolute error. For a direct method the measuring we can consider correct in range where resistance of voltmeter … (more greater or more less), then internal resistance of source.

10) Data: “___” _____20___. Work done by: ______ Work checked by:

( Surname, readable)

LABORATORY WORK № 2-4

Topic: POWER IN THE DIRECT CURRENT CIRCUIT

2. Goal of the work:

2.1. Study total power, useful power, and electrical efficiency dependence on current and external load resistance.

2.2. Finding the condition of matching of source to a circuit loading.

 

Main concepts

Types of power in a DC circuit

For direct current flowing in the circuit, there must be a source, where the extraneous forces create the excess of positive charges on one terminal of a device. Work of extraneous forces for moving the electric charge q between terminals inside the source, is equal (53):

А _EXTR = e q, (68)

where e – EMF of the source.

As the result charges get potential energy, which is equal Eq. If we close the circuit this potential energy will change into kinetic energy of electric charge's motion and the current will flow. The kinetic energy of electric charges will change into a heat, if there are no other energy transformations (for example, into mechanical in electric motors etc.). According to the energy conservation law, this total energy, which is being dissipated along the whole circuit during a time interval D t, is equal to work of extraneous forces for this time D W _T= А _EXTR.

Therefore a total power Р _T, which is being dissipated in electric circuit, is equal to work of extraneous forces per unit time:

. (69)

Using (68) and definition of current (19), we obtain:

. (70)

Useful power P _U is being dissipated inonthe external part of the circuit R (heat, light, mechanical work, etc.):

, (71)

where U_R – potential difference on the external part of the circuit R.

The power loss P _L due to heating of the internal resistance of source r:

, (72)

where U_r – potential difference on the internal part of the circuit r.

By magnitude of efficiency h we can estimate how the energy of the source is consumed. Efficiency of the source is the quantity, which is numerically equal to ratio of useful power P _U due to total power Р _T:

h = . (73)

If we take into account equations (70) and (71) we can write

h = . (74)