Study of full, useful power and efficiency of the current source. Investigation of the dependence of the power and efficiency of the current source from the external load What energy will be separated in the outer part of the chain

Ohma law for full chain:

I- The power of the current in the chain; E- electromotive strength of the current source included in the chain; R resistance to the external chain; R- Internal current source resistance.

Power allocated in the external chain

. (2)

From formula (2) it can be seen that with a short circuit of the chain ( R.®0) and with R.® This power is zero. With all other finite values R. power R 1\u003e 0. Consequently, the function R 1 has a maximum. Value R. 0, corresponding to the maximum power, can be obtained, differentiating P 1 along R and equating the first derivative to zero:

. (3)

From formula (3), taking into account the fact that R and R are always positive, and E? 0, after simple algebraic transformations, we get:

Hence, the power secreted in the outer chain reaches the greatest value with the resistance of the outer chain equal to the internal resistance of the current source.

In this case, the current in the chain (5)

equal to half of the short circuit current. In this case, the power secreted in the external chain reaches its maximum valueequal

When the source is closed to external resistance, the current flows and within the source and at the same time on the internal resistance of the source there is a certain amount of heat. The power spent on the selection of this heat is equal to

Consequently, the total power allocated in the entire chain is determined by the formula

= I 2.(R + R.) = IE. (8)

EFFICIENCY

EFFICIENCY The current source is equal . (9)

From formula (8) it follows that

those. R 1 changes with a change in current in the chain along a parabolic law and takes zero values \u200b\u200bat i \u003d 0 and at. The first value corresponds to the open circuit (R \u003e\u003e R), the second - short circuit (R<< r). Зависимость к.п.д. от силы тока в цепи с учётом формул (8), (9), (10) примет вид

Thus, kpd. Reaches the highest value H \u003d 1 in the case of an open circuit (i \u003d 0), and then decreases according to the linear law, turning to zero with a short circuit.

Power dependence P 1, P full \u003d EI and kp. The current source from the current in the circuit is shown in Fig.1.

Fig.1. I. 0 E / R.

From the graphs it can be seen that getting at the same time useful power and kp. It is impossible. When the power allocated at the external section of the chain p 1 reaches the greatest value, kp. At this point is 50%.

Method and measurement procedure

Collect the chain shown in Fig. 2. To do this, first click the left mouse button over the ED button. At the bottom of the screen. Move the mouse marker to the work part of the screen, where the points are located. Left-click in the operating part of the screen, where the source of ED will be located.

Further sequentially with the source of the resistor depicting its internal resistance (pressing the preload button at the bottom of the screen) and the ammeter (button there). Then placing similarly load resistors and a voltmeter, measuring voltage on the load.

Connect the connecting wires. To do this, press the Wire button at the bottom of the screen, then move the mouse marker to the schema working area. Click the left mouse button in the places of the screen of the screen, where the connecting wires must be.

4. Set the parameter values \u200b\u200bfor each item. To do this, click the left mouse button on the arrow button. Then click on this item. Move the mouse marker to the engine that appears, press the left mouse button and holding it down, change the value of the parameter and set the numeric value indicated in Table 1 for your option.

Table 1. Source parameters electrical chain

option

5. Install the resistance of the external circuit 2 Ohm, press the "Account" button and write down the readings of the electrical instruments in the appropriate lines of the table 2.

6. Consistently increase the resistance of an external chain by 0.5 Ohm from 2 Ohm to 20 ohms using the regulator engine and by pressing the "Account" button, write the readings of electrical instruments in Table 2.

7. Calculate according to formulas (2), (7), (8), (9) p 1, p 2, p full and h. For each pair of voltmeter and ammeter readings and write the calculated values \u200b\u200bin Table 2.

8. Build the graphics of the P 1 \u003d F (R), P 2 \u003d F (R), p 2 \u003d f (R), P is full \u003d f (R), H \u003d F (R) and U \u003d F (R) on one sheet of millimeter paper.

9. Calculate measurement errors and draw out the results of the experiments.

Table 2. Measurement and calculation results






P full, W

Questions and tasks for self-control

Record the Joule-Lenza law in integral and differential forms.
What is a short circuit current?
What is complete power?
As calculated by k.p.d. Source current?
Prove that the greatest useful power is allocated in the equality of external and internal chain resistance.
Is the statement true that the power secreted in the inner part of the chain is constant for this source?
A voltmeter attached to the clips of the battery panel of the pocket lamp, which showed 3.5 V.
Then the voltmeter was disconnected and the lamp was connected to its place, on the base of which it was written: p \u003d 30 W, u \u003d 3.5 V. Lamp did not burn.
Explain the phenomenon.
With an alternate closure of the battery on the resistance R1 and R2 in them in the same time an equal amount of heat was separated. Determine the internal resistance of the battery.

The dependence of the power and efficiency of the current source from the load

Instruments and accessories:laboratory panel, two batteries, milliammeter, voltmeter, variable resistors.

Introduction The most widespread sources of DC are galvanic elements, batteries, rectifiers. We connect to the current source that part that needs its electrical energy (light bulb, radio reception, microcalculator, etc.). This part of the electrical circuit is called a common word - load. Load has some electrical resistance R. and consumes from a source of current force I. (Fig.1).

The load forms the outer part of the electrical circuit. But there is an inside-dent part of the chain - it is actually the current source itself, it has electrical resistance r., It flows the same current I.. The boundary between the inner and external sections of the chain are the terminals "+" and "-" current source to which the consumer joins

In Figure 1, the current source is covered by a stroke circuit.

Current source with electromotive force E. Creates in a closed circuit current, the strength of which is determined ohm's law:

When current leaks R. and r. They allocate thermal energy, determined law Jojle Lenza.Power in the outer part of the chain R e. - External power

This power is useful.

Power in the inside R i. - Internal power. It is not available for use and therefore is lossessource power

Full Power source current R there is the sum of these two terms,

As can be seen from the definitions (2,3,4), each of the capacities depends on the flowing current and from the resistance of the corresponding part of the chain. Consider this dependence separately.

Power dependenceP. e. , P. i. , P. from current load.

Taking into account the Law of Ohm (1), complete power can be written as follows:

In this way, full source power is directly proportional current current.

The power released on the load ( external) there is

It is zero in two cases:

1) I \u003d 0. and 2) E - IR \u003d 0. (7)

The first condition is fair for open circuit when R. , the second corresponds to the so-called short closure source when the resistance of the external chain R. = 0 . At the same time, the current in the chain (see formula (1)) reaches the greatest value - short circuit current.

At the same time full Power becomes the highest

R nB = EI kZ. \u003d E. 2 / r.. (9)

However, it all stands out inside the source.

Find out under what conditions the external power becomes maxi Mal.. Power dependence P. e. From current is (see formula (6)) parabolic:

The position of the maximum function define from the condition:

dP. e. / di \u003d 0, dp e. / di \u003d e - 2ir.

Useful power reaches the maximum value at the current

what is half the short circuit current (8), (see Fig. 2):

External power with this current is

(12)

those. The maximum external power is the fourth part of the highest total source power.

The power released on the internal resistance at the current I. MAX is defined as follows:

, (13)

those. It is also one quarter of the greatest total power source power. Note that when current I. Max

P. e. = P. i. . (14)

When the current in the chain seeks the greatest value I. kZ. , Internal power

those. equal to the highest source power (9). This means that all the power of the source stands out on it internal Resistance, which, of course, is harmful from the point of view of the safety of the current source.

Characteristic point of character graphics P. e. = P. e. (I.) showing in Fig. 2.

Efficiency The operation of the current source is estimated to be efficient efficiency. The efficiency is the ratio of useful power to the total source power:

 = P. e. / P..

Using formula (6), the expression for the efficiency can be written as follows:

. (15)

From formula (1) it can be seen that E. – IR. = IR there is a voltage U. on external resistance. Consequently, efficiency

 = U./ E. . (16)

From the expression (15) it also follows that

 = (17)

those. The source efficiency depends on the current in the chain and tends to the greatest value equal to one, at a current I.  0 (Fig. 3) . With an increase in the current, the efficiency of the efficiency decreases according to the linear law and turns to zero with a short circuit when the current in the chain becomes the greatest I. kZ. = E./ r. .

From the parabolic nature of the dependence of external power from the current (6) it follows that one and the same power on the load P. e. It can be obtained at two different current values \u200b\u200bin the chain. From formula (17) and from the schedule (Fig. 3) it can be seen that in order to obtain from the source of greater efficiency, work is preferable at lower load currents, this coefficient is higher there.

2. dependence of powerP. e. , P. i. , P. from load resistance.

Consider addiction full, useful and internal power from external resistanceR. In the chain of the source with EMF E. and internal resistance r..

Full The power developed by the source can be written as follows if in formula (5) substitute the expression for the current (1):

So complete power depends on load resistance R.. It is the highest chain with a short circuit when the load resistance appeals to zero (9). With increasing load resistance R. Full power decreases, striving for zero with R.   .

On external resistance stands out

(19)

Exterior power R e. Makes part of full power R and its value depends on the resistance ratio R./(R.+ r.) . With a short closure, the external power is zero. With increasing resistance R. It increases first. For R.  r. The external power in magnitude is committed to complete. But the beneficial power itself becomes small, since the total power decreases (see formula 18). For R.  External power tend to zero as complete.

What should be the load resistance to get from this source maximum External (useful) power (19)?

Find the maximum of this function from the condition:

Deciding this equation we get R. Max \u003d. r..

In this way, in the outer chain, the maximum power is distinguished if its resistance is equal to the internal resistance of the current source. At the same time, the condition of the current in the chain is equal E./2 r., those. Half current short circuit (8). Maximum useful power with such resistance

(21)

which coincides with what was obtained above (12).

Power released on the internal resistance of the source

(22)

For R. P. i.  P., and when R.=0 reaches the greatest value P. i. NB = P. nB = E. 2 / r.. For R.= r. The internal power is half full, P. i. = P./2 . For R. r. It decreases almost the same as complete (18).

The dependence of the efficiency on the resistance of the outer part of the chain is expressed as follows:

 = (23)

The resulting formula implies that the efficiency tends to zero when the load resistance approaches zero, and the efficiency tends to the greatest value equal to one, with an increase in load resistance to R. r. . But useful power at the same time decreases almost like 1/ R. (see formula 19).

Power R e. reaches the maximum value when R. max = r., The efficiency is equal to the formula (23),  = r./(r.+ r.) = 1/2. In this way, the condition for obtaining maximum useful power does not coincide with the condition for obtaining the largest efficiency.

The most important result of the consideration is the optimal coordination of the source parameters with the nature of the load. Here you can allocate three areas: 1) R. r., 2)R. r., 3) R. r.. First The case takes place where low power is required from the source for a long time, for example, in electronic clock, microcalculators. The dimensions of such sources are small, the supply of electrical energy in them is small, it must be spent economically, so they should work with high efficiency.

Second The case is a short circuit in the load at which all the power of the source is highlighted in it and wires connecting the source with the load. This leads to their excessive heating and is a fairly common cause of fires and fires. Therefore, a short circuit of high power sources (dynamo machines, batteries, rectifiers) is extremely dangerous.

IN third case from the source want to get the maximum power at least a short Time, for example, when starting the engine of the car using an electric starter, the value of the efficiency is not so important. The starter is turned on for a short time. Long-term operation of the source in this mode is almost unacceptable, as it leads to a rapid discharge of a car battery, its overheating and other troubles.

To ensure the work of chemical sources of current in the desired mode, they are connected to a certain way in the so-called batteries. Elements in the battery can be connected sequentially, parallel to the mixed circuit. This or that compound scheme is determined by the load resistance and current consumption.

The most important operational requirement for energy installations is the high efficiency of their work. From formula (23) it can be seen that the efficiency tends to unity if the internal resistance of the current source is not enough compared to the load resistance

In parallel, you can connect elements having the same EMF. United n. identical elements, then from such a battery you can get a current

Here r. 1 - resistance of one element, E. 1 - EDC of one element.

Such a connection is beneficial to use at low voluntary load, i.e. for R. r.. Since the total internal resistance of the battery at a parallel connection decreases into n. once compared with the resistance of one element, it can be made close to the load resistance. Due to this, the efficiency of the source increases. Increases B. n. once and energy capacity of the battery of elements.

 r., it is more profitable to connect the elements in the battery sequentially. At the same time, EDC battery will be in n. once more EDC of one element and from the source you can get the required current

Purposethis laboratory work is experimental check The theoretical results obtained above the dependence of the total, internal and external (useful) power and efficiency of the source both from the strength of the current consumed and on the load resistance.

Description of installation. To study the operating characteristics of the current source, an electrical circuit is used, the diagram of which is shown in Fig. 4. Two NKN-45 alkaline batteries are used as a current source that are connected. follower - no in one battery Through resistor r. which simulates the internal contact of the source.

Its inclusion artificially Increases the internal resistance of the battery-larger, that 1) protects them from overload when switching to short circuit mode and 2) makes it possible to change the internal resistance of the source at the request of the experimenter. As a load (external chain resistance)
two variable resistor are rime R. 1 and R. 2 . (One rough adjustment, the other - thin), which provides smooth regulation of current in a wide range.

All devices are mounted on the laboratory panel. The resistors are fixed under the panel, their control knobs and terminals are displayed upwards, about which there are appropriate inscriptions.

Measurements. 1. Install the switch Pin neutral position, switch VCdisconnect. Pens resistors Turn counterclockwise until it stops (it corresponds to the greatest load resistance).

Collect the electrical circuit according to the scheme (Fig. 4), not attaching Current sources.

After checking the collected chain by a teacher or a laboratory assistant, attach batteries E. 1 and E. 2 By observing polarity.

Set short circuit current. To do this, place the switch P To position 2 (external resistance is zero) and using a resistor r. Set the Milliammeter arrow to the limit (rightmost) division of the instrument scale - 75 or 150 mA. Thanks to the resistor r. in the laboratory installation there ability to regulate Internal resistance of the current source. In fact, internal resistance is a permanent value for this type of sources and cannot be changed.

Put the switch P in the Regulation 1 , thereby turning on the external resistance (load) R.= R. 1 + R. 2 in the source chain.

Changing the current in the chain after 5 ... 10 mA from the largest to the smallest value using resistors R. 1 and R. 2 , write down the readings of the milliammeter and voltmeter (voltage on the load U.) in the table.

Put the switch P in neutral position. In this case, only a voltmeter is attached to the current source, which has a fairly large resistance compared to the internal resistance of the source, so the voltmeter reading will be a little less than EDC source. Since you do not have another opportunity to determine its exact value, it remains to take the testimony of a voltmeter for E.. (For more information about this, see Laboratory Work No. 311).

pP	ma.	P. e. ,	P. i. ,	R.,

Processing results. 1. For each current value, calculate:

full power by formula (5),

external (useful) power by formula

internal power from the ratio

resistance to the external section of the chain from the Ohm law R.= U./ I.,

CPD of the current source according to formula (16).

Build dependency graphics:

full, useful and internal power from current I. (on one tablet),

full, useful and internal power from resistance R. (also on one tablet); It is reasonable to build only part of the graph corresponding to its low-volume part, and drop 4-5 experimental points out of 15 in the high-altered region,

Efficiency of the source from the value of consumed current I.,

Efficiency from load resistance R..

From charts P. e. from I. and P. e. from R. determine the maximum useful power in the external chain P. e. Max.

From schedule P. e. from R. Determine the internal resistance of the current source r..

From charts P. e. from I. and P. e. from R. Find the CPD of the current source when I. max and for R. max .

Control questions

1. Draw the circuit of the electrical circuit used in operation.

2. What is the current source? What is the load? What is the inner plot of chains? Where does the external section of the chain begins and where does the outside section of the chain end? What is the variable resistor r. ?

3. What is called external, useful, internal, full capacity? What power is losses?

4. When useful power in this work is offered to count on the formula P. e. = IU., not the formula (2)? Justify these recommendations.

5. Create the experimental results obtained by you with the calculated shown in the methodological manual, both in the study of the dependence of the power of the current and the load resistance.

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Option 1
In the electrical circuit, the diagram of which is depicted in the figure, the measuring instruments are perfect, the voltmeter shows the value of the voltage of 8 V, and the ammeter is the value of the current 2 A. What amount of heat is highlighted in the resistor in 1 second?
The figure shows the circuit of the electrical circuit, including the DC source, the perfect voltmeter, key and resistor. The testimony of the voltmeter with a closed key is 3 times less than the voltmeter reading when the key is open.
It can be argued that the internal resistance of the current source
The figure shows the electrical chain. Voltmeter shows Voltage 2 V. Considering the ammeter and voltmeter ideal, determine the readings of the ammeter.

The figure shows the electrical chain. Ammeter and Voltmeter consider ideal. Voltmeter shows a voltage of 12 V. Ampmeret shows current strength

The figure shows the circuit of the electrical circuit. Through what resistor flows the greatest current?
The figure shows the circuit of the electrical circuit. By section AV flows permanent current 4 A. What voltage shows the perfect voltmeter if the resistance is 1 ohms?
The figure shows a diagram of a section of an electrical circuit consisting of three resistors R1, R2, R3. Which of the following drawings is given electrical circuit Is this plot of chain equivalent to the specified?

8. To the current source with EDC 9 and the internal resistance of 1 ohm, a connected resistor with an 8 ohm resistance resistance was connected; flat condenser. In the installed mode, the electrical field strength between the condenser plates 4. Determine the distance between its plates.

Option 2.
1. The student assembled the electrical circuit shown in the figure. What energy is available in the outer part of the circuit when current flows for 10 minutes? The required data is indicated in the scheme. Ammeter is considered ideal.
2. The current source has EMF 6 V, the internal resistance of 1 ohms, R1 \u003d 1 Ohm R2 \u003d R3 \u003d 2 ohms. What strength current flows through the source?

3. The figure shows an electrical circuit. Ammeter and Voltmeter consider ideal. Voltmeter shows a voltage of 12 V. Ampmeret shows current strength

4. The figure shows the electrical circuit. Ammeter and Voltmeter consider ideal. Voltmeter shows Voltage 2 V. Ampmeret Shows current strength

5. Figure shows the circuit of the electrical circuit. Through what resistor flows the smallest current?
6HA Figure shows the circuit of the electrical circuit. By section AV flows permanent current 6 A. What voltage shows the perfect voltmeter if the resistance is 1 ohms?
7.
The figure shows a diagram of a section of an electrical circuit consisting of three resistors R1, R2, R3. Which of the following drawings shows the electrical diagram of this section of the chain equivalent to the specified one?

8. To the current source with EDC 10 and the internal resistance of 1 Ω, a parallel connected resistor with an 8th resistance and a flat condenser was connected, the distance between the plates of which is 4 cm. What is the electric field strength between the condenser plates?

Applied files

1. What is the time of passage of current by force of 5 A according to the conductor, if at a voltage at its ends 120V in the conductor the amount of heat equal to 540 kJ? (Give the answer in seconds.)

2. In the electric heater with the unchanged resistance of the spiral, through which the constant current flows, during the time t. The amount of warmth is distinguished Q.. If current and time t. Enlarge twice, how many times the amount of heat released in the heater will increase?

3. Resistor 1 with an electrical resistance of 3 Ohms and a resistor 2 with an electrical resistance of 6 ohms are included in the DC circuit. What is equal to the ratio of the amount of heat released on the resistor 1, to the amount of heat released on the resistor 2 for the same time?

4. The figure shows a timeline of the current force in the incandescent lamp from the voltage on its terminals. What is the power of the current in the lamp at a voltage of 30 V? (Give the answer in watts.)

The student assembled the electrical chain shown in the picture. What energy is available in the outer part of the circuit when current flows for 10 minutes? (Answer express to CJ. The required data is indicated in the scheme. Ampmeret is considered ideal.)

6. To the current source with EDC 2, the capacitor with a capacity of 1 μF is connected. What work did the source do when charging the condenser? (Answer in the ICD.)

7. To the current source with EDC 2, the capacitor with a capacity of 1 μF is connected. What heat is highlighted in the circuit in the process of charging the condenser? (Give the answer to ICJ.) Effects of radiation neglected.

8. To the perfect current source with EDC 3 in the capacitor with a capacity of 1 μF once through a resistor And the second time - through the resistor How many times in the second case the heat released on the resistor, more compared to the first? Radiation neglected.

9. To the current source with EDC 4 V and internal resistance Connected load resistance. What should it be equal to the source efficiency to be 50%? (Answer in Omah.)

10. In the electrical circuit, the diagram of which is depicted in the figure, the measuring instruments are perfect, the voltmeter shows the value of the voltage of 8 V, and the ammeter is the value of the current 2 A. What amount of heat is highlighted in the resistor in 1 second? (Give the answer in Joules.)

11. The room is illuminated by four the same parallel light bulbs. Electricity consumption per hour is equal Q.. What should be the number of parallel light bulbs so that electricity consumption per hour is equal to 2 Q.?

12. Electric kettle with a power of 2.2 kW is designed to include in an electrical network voltage 220 V. Determine the current in the heating element of the kettle when it works in such a network. Answer to bring in amperes.

13. On the housing of the electrician-roster there is an inscription: "220 V, 660 W". Find strength consumed by Rosther. (Answer give in amperes.)

14. On the base of the electric incandescent lamp, it is written: "220 V, 60 W". Two such lamps are connected in parallel and connect to 127 V. voltage What power will be highlighted in two lamps with such a connection method? (Answer to give in watts, rounded to integer.) When solving the problem, consider that the lamp resistance does not depend on the voltage applied to it.

15. In the base of the electric incandescent lamp, it is written: "220 V, 100 W." Three such lamps are connected in parallel and connected to voltage 127 V. What power will be highlighted in three these lamps with such a connection method? (Answer to give in watts, rounded to integer.) When solving the problem, consider that the lamp resistance does not depend on the voltage applied to it.

16. In the school laboratory there are two conductor of round-section. The resistivity of the first conductor is 2 times the resistance of the second conductor. The length of the first conductor is 2 times longer than the length of the second. When these conductors are connected to the same sources of constant voltage for the same time intervals in the second conductor, the amount of heat is 4 times greater than in the first one. What is the ratio of the radius of the second conductor to the radius of the first conductor?

17. In the school laboratory there are two conductor of round-section. The resistivity of the first conductor is 2 times the resistance of the second conductor. The length of the first conductor is 2 times longer than the length of the second. When connecting these conductors to the same sources of constant voltage for the same time intervals in the second conductor, the amount of heat is 4 times smaller than in the first. What is the ratio of the radius of the first conductor to the radius of the second conductor?

18. R. 1, included in the electrical circuit, the diagram of which is shown in the figure? (Answer to give in watts.) R. 1 \u003d 3 ohms, R. 2 \u003d 2 ohms, R.

19. What power is highlighted in the resistor R. 2, included in the electrical circuit, the diagram of which is depicted in the figure? (Answer to give in watts.) R. 1 \u003d 3 ohms, R. 2 \u003d 2 ohms, R. 3 \u003d 1 Ohm, EMF of the 5 V source, the internal resistance of the source is negligible.

20. R. \u003d 16 ohms, and voltage between points A. and B.is the 8th century? Answer to bring in watts.

21. What power is highlighted in the chain section, the diagram of which is shown in the figure, if R. \u003d 27 Ohm, and voltage between points A. and B.is the 9th century? Answer to bring in watts.

22. I. \u003d 6 A. What is the current of the current that the ammeter shows? (Give the answer in amperes.) Amplimeter resistance to neglect.

23. Resistor with resistance is connected to the current source with EDC and internal resistance If you connect this resistor to the current source with EDC and internal resistance Which time the power allocated in this resistor will increase?

24.

I. U. on the lamp. Such a lamp was connected to a source of permanent voltage 2 W. What kind of work will the electric current in the filament of the lamp inclusion in 5 seconds? Answer express in J.

25.

The graph shows the experimentally obtained dependence of the current I.flowing through the incandescent lamp, from voltage U. on the lamp. Such a lamp was connected to a source of constant voltage of 4 V. What kind of work will the electric current in the filament of the lamp inclousing in 10 seconds? Answer express in J.

26. Through the chain section (see Figure) there is a permanent current I. \u003d 4 A. What strength will show the perfect ammeter included in this chain, if the resistance of each resistor r. \u003d 1 ohms? Answer express in amperes.

27. A point positive charge of a value of 2 μCl is placed between two extended plates, uniformly charged with a variety of charges. The electric field strength module created by a positively charged plate is 10 3 kV / m, and the field created by a negatively charged plate is 2 times more. Determine the electrical power module that will act on the specified point charge.

28. The point positive charge of the value of 2 μCl is placed between two extended plates, uniformly charged positive charges. The voltage modulus of the electric field created by one plate is 10 3 kV / m, and the field created by the second plate is 2 times more. Determine the electrical power module that will act on the specified point charge. Answer Give Newton.

29.

FROM, resistance resistor R. and K. Condenser is charged to voltage U. \u003d 20 V. Charge on capacitor plates is equal q. \u003d 10 -6 cl. What amount of heat is highlighted in a resistor after closing the key to? Answer express the ICD.

30.

The figure shows the circuit circuit consisting of capacitor capacitance FROM, resistance resistor R. and K. Capacity Capacitor C. \u003d 1 μF, and it is charged to voltage U. \u003d 10 V. What amount of heat is highlighted in the resistor after closing the key to? Answer express the ICD.

31. The fuse of the electricity meter in the apartment network voltage 220V is equipped with an inscription: "6 A". What is the maximum total power of electrical devices that can be simultaneously included in the network so that the fuse is not melted? (Answer in watts)

Laboratory work number 3.7.

Research of useful power and efficiency of current sources

Surname I.O. _____________ Group ______ Date ______

Introduction

The purpose of this work is to experimentally check the theoretical conclusions about the dependence of the useful power and the efficiency of the current source from the load resistance.

The electrical circuit consists of a current source, supplying wires and loads or consumer of the current. Each of these elements of the chain has resistance.

The resistance of the supply wires is usually very small, so they can be neglected. In each section of the chain, the energy source energy will be consumed. A very important practical importance is the question of the expedient expenditure of electrical energy.

The total power P, highlighted in the chain, will be made from the capacities allocated in the outer and inner parts of the chain: P \u003d i 2 · r + i 2 · r \u003d i 2 (R + R). As I (R + R) \u003d εT. P \u003d i · ε,

where R is external resistance; R - internal resistance; ε - EMF current source.

Thus, the total power secreted in the circuit is expressed by the course of the current for the EMF element. This power is allocated due to any third-party sources; Such energy sources can be, for example, chemical processes occurring in the element.

Consider how the power allocated in the circuit depends on the external resistance R to which the element is closed. Suppose that the element of this EMF and this internal resistance R closes the external resistance R; Determine the dependence on R full power P, is allocated in the chain, the power of P A, isolated in the outer part of the chain and the efficiency.

The strength of the current I in the chain is expressed according to the law of Oma by the ratio

Full power secreted in the chain will be equal to

With an increase in R, the power drops, striving asymptotically to zero with an unlimited increase of R.

The power released in the outer part of the chain is equal to

It can be seen that the useful power of p a is zero in two cases - at r \u003d 0 and r \u003d ∞.

Exploring the function Р А \u003d f (r) to extremum, we obtain that R a reaches a maximum at r \u003d r, then

To ensure that the maximum power of P A is obtained at R \u003d R, take the derivative of P A by external resistance

From

By the maximum condition, the equality is required to zero the first derivative

r 2 \u003d R 2

R \u003d R.

You can make sure that under this condition we will receive a maximum, and not at least for P A, defining the sign of the second derivative.

The efficiency of the efficiency (efficiency) η of the source of the EMF is the value of the ratio of the power of P A, which is released in the outer chain, to the total power of the P, developed by the source of the EMF.

In essence, the efficiency of the EMF source indicates which proportion of third-party work is transformed into electrical energy and is given to the outer chain.

Expressing power through current I, the difference of potentials in the outer circuit U and the magnitude of the electromotive force ε, we obtain

That is, the efficiency of the EDC source is equal to the ratio of the external chain to the EMF. In the conditions of applicability of the Ohm Law, you can further replace U \u003d IR; ε \u003d i (R + R), then

Therefore, in the case when all the energy is consumed on Lenz-jowle heat, the efficiency of the EDC source is equal to the ratio of external resistance to the full chain resistance.

At r \u003d 0 we have η \u003d 0. With increasing R, the efficiency increases, tends to the value η \u003d 1 with an unlimited increase of R, however, the power released in the outer chain tends to zero. Thus, the requirements for the simultaneous preparation of maximum useful power at the maximum efficiency are impracticable.

When R A reaches a maximum, then η \u003d 50%. When efficiency η is close to one, the useful power is small compared with the maximum power that this source could develop. Therefore, to increase the efficiency, it is necessary to reduce the internal resistance of the EMF source, for example, a battery or a dynamo machine.

In the case of R \u003d 0 (short circuit) R a \u003d 0 and all power is highlighted within the source. This can lead to overheating of the inner parts of the source and the derivation of it. For this reason, short circuits of sources (dynamo machines, rechargeable batteries) are not allowed!

In fig. 1 curve 1 gives the dependence of the power of P A, isolated in the outer chain, from the resistance of the outer part of the circuit R; Curve 2 gives the dependence on R full power P; Curve 3 - the course of the efficiency of η from the same external resistance.

Procedure for performing work

1. Read the scheme on the stand.

2. Install the resistance r \u003d 100 ohm using the store.

3. Close the key K.

4. Current measurements in the chain sequentially for various nine resistance at the resistance store, ranging from 100 ohms and higher. Make in the table the results of measurements of current force, expressing them in amperes.

5. Turn off the key K.

6. Calculate for each resistance P, R A (in watts) and η.

7. Build graphs P, R A and η from R.

Control questions

1. What is called an efficiency of the EMF source?

2. Remove the Formula of the efficiency of the EDC source.

3. What is the useful power of the EMF source?

4. Remove the formula for the useful power of the EDC source.

5. What is the maximum power allocated in the external chain (RA) MAX?

6. With what value r full power P released in the chain maximal?

7. What is the efficiency of the EMF source at (RA) MAX?

8. Research function (RA) \u003d f (R) on extremum.