Examples of problem solving. Investigation of the total, useful power and efficiency of the current source Studying the laws of connecting resistors, the student collected
OHM'S LAW FOR THE FULL CHAIN:
I is the current in the circuit; E is the electromotive force of the current source included in the circuit; R is the resistance of the external circuit; r is the internal resistance of the current source.
POWER RELEASED IN THE EXTERNAL CIRCUIT
. (2)
From formula (2) it can be seen that with a short circuit of the circuit ( R®0) and for R® this cardinality is equal to zero. For all other end values R power R 1\u003e 0. Therefore, the function R 1 has a maximum. Value R 0, corresponding to the maximum power, can be obtained by differentiating P 1 over R and equating the first derivative to zero:
. (3)
From formula (3), taking into account that R and r are always positive, and E? 0, after simple algebraic transformations we get:
Hence, the power released in the external circuit reaches its maximum value when the resistance of the external circuit is equal to the internal resistance of the current source.
In this case, the current in the circuit (5)
equal to half the current short circuit... In this case, the power released in the external circuit reaches its maximum value equal to
When the source is closed to an external resistance, then the current flows inside the source and a certain amount of heat is released on the internal resistance of the source. The power spent on the release of this heat is
Consequently, the total power released in the entire circuit is determined by the formula
= I 2(R + r) = IE (8)
EFFICIENCY
EFFICIENCY current source is 
. (9)
From formula (8) it follows that
those. R 1 changes with a change in the current in the circuit according to the parabolic law and takes zero values \u200b\u200bat I \u003d 0 and at. The first value corresponds to an open circuit (R \u003e\u003e r), the second to a short circuit (R<< r). Зависимость к.п.д. от силы тока в цепи с учётом формул (8), (9), (10) примет вид
Thus, the efficiency reaches the maximum value h \u003d 1 in the case of an open circuit (I \u003d 0), and then decreases linearly, turning to zero during a short circuit.
Dependence of capacities Р 1, Р total \u003d EI and efficiency current source from the current in the circuit are shown in Fig. 1.
Fig. 1. I 0 E / r
It can be seen from the graphs that it is possible to simultaneously obtain useful power and efficiency. impossible. When the power released in the outer section of the P 1 circuit reaches the highest value, the efficiency is at this moment is equal to 50%.
MEASUREMENT PROCEDURE AND ORDER
Assemble the circuit shown in fig. 2. To do this, first left-click on the e.m.f. button. at the bottom of the screen. Move the mouse marker to the working area of \u200b\u200bthe screen where the points are located. Left-click in the working area of \u200b\u200bthe screen where the source of emf will be located.
Place further in series with the source a resistor representing its internal resistance (by first pressing the button at the bottom of the screen) and an ammeter (button in the same place). Then position the load resistors and a voltmeter that measures the voltage across the load in the same way.
Connect the connecting wires. To do this, click the wire button at the bottom of the screen, and then move the mouse marker to the working area of \u200b\u200bthe circuit. Click the left mouse button in the places of the working area of \u200b\u200bthe screen, where the connecting wires should be.
4. Set parameter values \u200b\u200bfor each item. To do this, left-click on the arrow button. Then click on this item. Move the mouse marker to the slider of the appeared regulator, press and hold the left mouse button, change the parameter value and set the numerical value indicated in Table 1 for your variant.
Table 1. Initial parameters of the electrical circuit
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5. Set the resistance of the external circuit to 2 Ohm, press the "Count" button and write down the readings of the electrical measuring instruments in the corresponding lines of Table 2.
6. Using the regulator slider, increase the resistance of the external circuit by 0.5 Ohm from 2 Ohm to 20 Ohm in succession and, pressing the "Count" button, write down the readings of electrical measuring instruments in Table 2.
7. Calculate by the formulas (2), (7), (8), (9) Р 1, Р 2, Р total and h for each pair of voltmeter and ammeter readings and record the calculated values \u200b\u200bin Table 2.
8. Build on one sheet of graph paper the graphs of dependence P 1 \u003d f (R), P 2 \u003d f (R), P full \u003d f (R), h \u003d f (R) and U \u003d f (R).
9. Calculate measurement errors and draw conclusions based on the results of the experiments.
Table 2. Results of measurements and calculations
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P full, W |
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Questions and tasks for self-control
- Write down the Joule-Lenz law in integral and differential forms.
- What is short circuit current?
- What is Apparent Power?
- How is efficiency calculated? current source?
- Prove that the greatest useful power is released when the external and internal resistances of the circuit are equal.
- Is it true that the power released in the internal part of the circuit is constant for a given source?
- A voltmeter was connected to the terminals of the flashlight battery, which showed 3.5 V.
- Then the voltmeter was disconnected and a lamp was connected in its place, on the base of which it was written: P \u003d 30 W, U \u003d 3.5 V. The lamp did not burn.
- Explain the phenomenon.
- With the alternate closure of the battery to the resistances R1 and R2, an equal amount of heat was released in them for the same time. Determine the internal resistance of the battery.
1. B 15 No. 1404. How to change a co-opposing section of the chain AB, depicting-ra-femin-no-go on ri-sun-ke, if the key TO to open?
Co-contra-le-tion of each resistor is equal to 4 ohms.
1) decrease by 4 ohms
2) decrease by 2 ohms
3) increase-whether-cheat-Xia by 2 ohms
4) increase-whether-cheat-Xia by 4 ohms
Decision.
Until the release of the key, depicted on the ri-sun-ke ver-ti-kal-no co-contra-le-niya za-ko-ro-che-ny, diagram presents-becomes-la-is just re-zi-stor R.
If you open the key, the "ver-t-cal-nye" co-opposites will not-re-become-chicks and the scheme will-no-represent to be after-to-va-tel-but co-unity-not-re-zi-st-ra R with two paral-lel-but co-unified-nen-mi re-zi-sto-ra-mi R... Next-to-va-tel-but co-contra-lection of the chain section after opening the key will be equal to:
Thus, the co-contraction of the section of the circuit increased by 2 ohms.
Correct answer: 3.
2. B 15 No. 1408. On the photo-to-graphy - an electric-three-che-circuit.
The volt-meters are given in volts. What will the volt-meters be equal to, if it is connected paral-lel-but- zi-store-ru 2 Ohm? Consider the volt meter as ide-al-ny.
Decision.
According to-but-for-k-nu Ohm, the current strength, co-contra-lection of the conductor-nik-ka and the-strand between its ends of the connection us with-ot-n-she-ni. Since res-z-stor 1 Ohm and res-z-stor 2 Ohm are connected after-to-va-tel-but, current strength, te-to-shch-go through them, ow-pa-da-et. Left-to-va-tel-but, ideal-al-volt-meter, connected pa-ra-lel-but to the res-zi-store-ru 2 Ohm, it seems to - spice
Correct answer: 3.
3. B 15 No. 1409. On ri-sun-ke, there is a section-drain of a chain of a hundred-yang-but-th current.
What is the co-opposition of this site, if?
Decision.
Ucha-stock represents itself after-to-va-tel-nye co-unity-not-re-zi-st-ra r and two paral-lel-but-co-unified res-d-rovs 3 r... Next-to-va-tel-but, the co-contra-lection of this site is equal.
Correct answer: 2.
4. B 15 No. 1410. On the photo-to-graphy - an electric-three-che-circuit.
By-ka-za-niya included in the chain of am-per-meter are given in am-pe-rah. What kind of voltage does an ideal volt meter look like if it is connected in parallel-lel-but re-zi-store-ru 3 Ohm?
Decision.
According to-but-for-k-nu Ohm, the current strength, co-contra-lection of the conductor-nik-ka and the-strand between its ends of the connection us with-ot-n-she-ni. All re-si-sto-ry are connected after-to-va-tel-but, which means, through them all flows the same current with a force of 0.8 A. So, the ideal volt meter, connected paral-lel-but to the 3 Ohm resistor, seems to be desire
Correct answer: 3.
5. B 15 No. 1411. R.
TO equally
Decision.
After closing the key, the right half of the circuit will turn out to be over-short, the circuit will be vi-wa-lent-ta two connected pa-ral-lel-no re-zi-sto-ram.
Full co-contra-lection of the site when the key is closed TO equals:.
The correct answer is: 1.
6. B 15 No. 1412. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
Full co-contra-lection of the site when the key is closed TO equally R.
Correct answer: 2.
7. B 15 No. 1413. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed K equally:
Decision.
After the key is closed, the scheme will be a parallel co-contraction of the resistor with two after-to-va tel-but co-united-n-n-mi-zi-sto-ra-mi.
Full co-contra-lection of the site when the key is closed K equally:
The correct answer is: 1.
8. B 15 No. 1414. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed K equally:
Decision.
After closing the key, the right half of the circuit will turn out to be over-short, the circuit will be vi-wa-len-ta two connected after-to-va-tel-but-zi-sto-ram.
Full co-contra-lection of the site when the key is closed K equals:.
Correct answer: 3.
9. B 15 No. 1415. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
Full co-contra-lection of the site when the key is closed TO equals 0.
The correct answer is: 1.
10. B 15 No. 1417. The flow-off of the chain is one hundred and one of three after-to-va-tel-but-co-unified resis-tors, co-opposed to co- rykh are equal r, 2r and 3r The co-contrast of the site is reduced by 1.5 times, if you remove from it:
1) the first re-zi-store
2) second re-zi-store
3) third re-zi-store
4) the first and second re-si-ry
Decision.
Ucha-drain of the chain, consisting of three subsequent-to-va-tel-but-unified resistors with co-contra-le-ni i-mi r, 2r and 3 r, has co-contra-le-tion. To reduce this co-opposition by 1.5 times, that is, to make it equal:
not-about-ho-di-mo remove co-contra-le-tion 2 r... Left-to-va-tel-but, you need to remove the second re-zi-store.
Correct answer: 2.
11. B 15 No. 1419. On the ri-sun-ke, along the-ka-zan, a section of the chain is a hundred-yang-but-th current, containing 3 re-zi-st-ra.
If the co-opposition of each resistor is 21 Ohm, then the co-opposition of the entire chain section:
Decision.
The chain run-off is two after-to-va-tel-but-co-unified res-zi-st-ra, to which-eye pa-ral-lel -but under-co-united-nen one more. Next-to-va-tel-but, co-contra-lection of the entire site is equal to:
Correct answer: 3.
12. B 15 No. 1421. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
1 way:
After the key is closed, the left-hand side of the circuit will turn out to be over-short, the circuit will be equal to wa-lent-that just one-no-mo re-zi-st-ru.
Full co-contra-lection of the site when the key is closed TO equally R.
Correct answer: 2.
2 way:
Consider the left-hand side of the diagram after closing the key. She is a parall-lell-ness of a re-zi-st-ra with a co-oppo-le-no R and co-uni-ni-tel-no-pro-in-yes with a pre-not-shy-little co-against-le-no. Therefore, according to the righteousness of the account of the general co-oppo-ness of pa-ral-lel-but co-unified pro-water kov on-lo-cha-em, that co-versus left on-lo-vin-ki is equal.
Thus, the co-opposition of the left-hand side of the circuit is equal to zero. From here-and-yes, we will immediately see that the complete co-contraction of the scheme after the key is closed is equal.
13. B 15 No. 1422. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
After the key is seated, the scheme will be eq-vi-va-lent-ta pa-ral-lel-no-mu co-unification of two re-zi-sts.
Full co-contra-lection of the site when the key is closed TO equally: .
The correct answer is: 1.
14. B 15 No. 1423. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
After the key is closed, the left-hand side of the circuit will turn out to be over-short, the circuit will be equal to wa-lent-that just one-no-mo re-zi-st-ru.
Full co-contra-lection of the site when the key is closed TO equally R.
Correct answer: 2.
15. B 15 No. 1424. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
After closing the key, the left-hand side of the circuit will turn out to be over-short, the half-chiv-sha-I-Xia scheme will be equal va-lent-ta after-to-va-tel-no-mu co-unity-not-niyu three re-zi-st-ditch.
Full co-contra-lection of the site when the key is closed TO equals:.
Correct answer: 4.
16. B 15 No. 1425. On the section of the chain, depicted on the ri-sun-ke, the co-contraction of each of the re-zi-sts is equal to R.
Full co-contra-lection of the site when the key is closed TO equally:
Decision.
After closing the key, the scheme will be eq-vi-va-lent-ta after-to-va-tel-no-mu-co-uni-ni of two pairs of paral-lel-no with -dinned-n-n-ny-zi-st-ditch.
Full co-contra-lection of the site when the key is closed TO equally:
Correct answer: 2.
17. B 15 No. 1426. Calculate-tai-te common co-contra-tion of the electric-three-che-chain, represented on the rice-sun-ke.
Decision.
The electric-three-che-chain is an after-to-great co-unity of the resistor 1 Ohm with paral-lel- but co-united-n-ny-mi re-zi-sto-ra-mi 2 Ohm and another res-zi-store-rum 1 Ohm. The co-contrast of such a scheme is equal to:
Correct answer: 3.
18. B 15 No. 1427. Co-opp-lee chain on rice-sun-ke is equal to:
Decision.
The elec-three-che-chain is an after-to-va-tel-co-unity-non-resistive 2 Ohm with paral-lel- but co-united-n-n-mi re-zi-sto-ra-mi 6 ohms and 3 ohms. The co-contrast of such a scheme is equal to:
Correct answer: 3.
19. B 15 No. 1436. What will be the co-opposition of the chain section (see rice-su-nok), if the key TO close?
(Each of the reso-moats has a co-contra-lection R.):
Decision.
After closing the key, the clem-we will be-horrified for-k-ro-chen-mi.
Full co-contra-lection of the site when the key is closed TO equals 0.
20. B 15 No. 3230. On the ri-sun-ke, there is an electric-three-che-chain. Am-per-meter and volt-meter count-tay-te ide-al-ny-mi. Volt-meter on-ka-zy-wa-e-on-off 2 IN
Decision.
Rheo-stat, two resistors with co-against-le-no-I-mi 4 Ohm and 6 Ohm and am-per-meter are connected after-before- va-tel-but, and this means, through them one-on-one current flows. Using Ohm's law for a section of the circuit, determine the current strength, te-ku-shche-go through the res-zi-store with co-contra-le-ni 4 Ohm:. It is precisely such a current strength and, ka-zy-va-et am-per-meter.
21. B 15 No. 3231. On the ri-sun-ke, there is an electric-three-che-chain. Volt-meter on-ka-zy-wa-e-on-off 2 IN... Considering the am-per-meter and the volt-meter of the ide-al-ny-mi, determine the de-li-te according to the am-per-meter.
Decision.
Rheo-stat, two resistors with co-against-le-no-I-mi 4 Ohm and 10 Ohm and am-per-meter connected after-before- va-tel-but, and this means, through them one-on-one current flows. Using Ohm's law for a section of the circuit, determine the current strength, te-ku-shche-go through the res-zi-store with co-contra-le-ni 10 Ohm: Names -but such amperage and on-ka-zy-wa-et am-per-meter.
22. B 15 No. 3232. On the ri-sun-ke, there is an electric-three-che-chain. Am-per-meter and volt-meter count-tay-te ide-al-ny-mi. Volt-meter for-ka-zy-wa-et for-voltage-12 V. Am-per-meter for-ka-zy-wa-et amperage
Decision.
Rheo-stat, two resistors with co-against-le-no-I-mi 4 Ohm and 6 Ohm and am-per-meter are connected after-before- va-tel-but, and this means, through them one-on-one current flows. The volt meter is connected to the section of the circuit, representing itself after the next-to-great connection of two res-zi-hundred -rov. The total co-opposition of this section of the chain is equal. Using Ohm's law, determine the current strength, te-ku-shche-go through the res-si-ry:. It is precisely such a current strength and, ka-zy-va-et am-per-meter.
23. B 15 No. 3233. On the ri-sun-ke, there is an electric-three-che-chain. Am-per-meter and volt-meter count-tay-te ide-al-ny-mi. Volt-meter on-ka-zy-wa-et on-strand-ing 12 IN... Am-per-meter by-ka-zy-va-et amperage
Decision.
Rheo-stat, three resistors with co-against-le-no-i-mi 4 ohm, 5 ohm and 6 ohm and am-per-meter connected after -do-va-tel-but, and that means, one-on-one current flows through them. The volt meter is connected to the section of the circuit, representing itself after the following-to-important connection of three res-zi-hundred -rov. The total co-opposition of this section of the chain is
Using Ohm's law, determine the current strength, te-ku-shche-go through the res-s-ry: ... It is precisely such a current strength and, ka-zy-va-et am-per-meter.
24. B 15 No. 3331. How-to-oppose the section of the chain depicted on the rice-sun-ke, if the co-opposed to each re-zi-ra r?
Decision.
The chain run-off is three after-to-va-tel-but-co-unified re-zi-st-ra, to some paral-lel -but under-co-united-nen one more same re-zi-store. Left-to-va-tel-but, co-oppo-lection of the whole site is equal
25. B 15 No. 3332. Two re-zi-sto-ra are included in the electric-three-che-chain pa-ra-lel-but, as in-ka-za-but on the ri-sun-ke. The knowledge of the current strength in the res-zi-sts,. For co-contra-ley res-z-st-ditch right-ved-l-in co-relation
Decision.
When pa-ra-lel-nom co-uni-ne-nii na-pry-niya-niya on re-zi-sto-s co-pa-da-yut. According to-but-for-ko-well Om for a section of the chain: Left-to-va-tel-but,
26. B 15 No. 3379. On the ri-sun-ke pri-ve-de-na pho-to-gra-fi of the electrical circuit, co-assembled by the teacher for the study of the -vi-si-bridging of the current strength, pro-ho-dya-shche-go through the res-zi-stor, from the on-line-on it. In order to pro-te-cal current with a force of 1 A through the resistor, the current on it must be equal to:
Decision.
From the rice-sun-ka, you can determine the am-per-meter and volt-meter. One-on-one pre-va-ri-tel-but it is necessary to remember the determination of the price of de-le-niya from-me-ri-tel-no-bo-ra. The price of a division can be determined by dividing the distance between the closest numbers on the scale by the number of divisions between them. For example, for a volt meter we have:.
The photo-graph shows that when the voltage is applied to the resistor at 4.3 V, the current through it is 0.75 A. re-zi-store-re and the current strength through it pro-por-tsi-o-nal-us, according to-but-for-ko-well Om,. Left-to-va-tel-but, in order for a current of 1 A to flow through the resis-stor, not-about-ho-di-mo is attached to it to-live.
27. B 15 No. 3381.
The disciple took the electrical circuit, depicted in the ri-sun-ke. What energy do you get in the outer part of the circuit when the current flows for 10 minutes? Not-about-ho-di-my data are indicated on the diagram. Consider am-per-meter as ide-al-ny.
Decision.
According to-but-for-to-well Jo-u-la-Lenz, the energy of you-de-la-yu-shcha-I-Xia for the time with pro-te-ka-nii through co-against -lee-nie ve-li-chi-noy current is equal. In the diagram, the teacher of the res-zi-store-ry 2 Ohm and 4 Ohm co-one-not-us after-to-va-tel-but, and that means, their common co-against -lee is equal to Ohm. The current strength is 1 A. Thus, in the external circuit in 10 minutes you will be released.
28. B 15 No. 3394.
The chain-run-off consists of two one-on-one paral-lel-but-co-one-on-one resistors and, each with co-contra -le-ni-em 2 Ohm, and res-zi-st-ra with co-oppo-le-ni-em 3 Ohm.
The total co-opposition of the chain section is equal to:
Decision.
Sna-cha-la find a common co-contra-lection of two paral-lel-but co-unified re-zis-movers and: Ohm... Re-zi-store under-co-united-nen to them after-to-va-tel-but. Next-to-va-tel-but the total co-contrast of the chain section is Ohm.
29. B 15 No. 3421.
Two resistors are included in the electrical circuit after-to-va-tel-but. How-to-but-sit-Xia according to-the-for-the-ide-al-volt-meters, depicted on the rice-sun-ke:
Decision.
There is no current flowing through the ideal volt meter, it has an infinite co-opposition, and for that reason it does not affect the ve-li-chi - currents and currents in the network. With the subsequent co-unity, one-on-one current flows through the re-zi-sto. According to-but-for-k-nu Om, the current strength through the conductor-nick and to-direct-ing-ness, attached to it, is connected with-from-n-she -n-eat. In this way, because of the volt-meters, they are connected with-with-but-she-ni:.
30. B 15 No. 3422.
Diagram of an electrical circuit in a ka-za-na on a rice-sun-ke. When the key K is open, the ideal volt meter is 8 V. When the key is turned on, the volt meter is 7 V. Co - the resistance of the external circuit is 3.5 ohms. What is the EMF of the current source?
Decision.
Since-ku-ka-za-volt-meter, under-co-unified-n-go to the source of-no-ku me-nya-yut-Xia when za-we-ka -nii key, this means that the source-source is not ideal, and its inner-ren is not co-opposed to it from zero. In the second case, it is less, since current flows through the source, and part of the flow is pa-da-et on the inner-wren-against-against-ley. In the first case, there is no current in the network. More precisely, the current was, while pro-is-ho-di-la charge-ka con-den-sa-to-ra, but after the con-den-sa-tor rya-dil-sya, the current pre-collapsed. And that means, in the first case, the volt-meter according to the EMF is the source. It is equal to 8 V.
31. B 15 No. 3424.
On the pic-sun-ke, there is a diagram of an electrical circuit. What will happen with the common co-versus chain when you lock the key K? Co-opp-chain
1) increase-whether-chit-Xia with any values \u200b\u200band
2) decreases for any values \u200b\u200band
3) decrease, only if
4) u-u-chit-Xia, only if
Decision.
When-we-ka-nii key, two re-zi-sto-ras are-horror-Xia under-key-chen-mi pa-ra-lel-no. With a parallel-lell-nn co-uni-ne-nii of two resis-tors, the total co-opposition is always less than the co-opposition any of them. Pro-ve-rim this, for example, for co-oppo-le-ny, for the second pro-ve-ry-ia-ia-lo-gich-no. Ras-smot-rim difference:
Correct answer: 2.
32. B 15 No. 3471. On the ri-sun-ke pri-ve-de-na electric-three-che-chain. What is the work of an electric current for 5 minutes of current flow in the section of the circuit, to which the volt meter is connected? ?
Decision.
The ra-bo-that of the current during the time is connected with the direct-current and with the current strength with-with-but-she-ni. From the rice-sun-ka it is clear that the voltage is equal, and the current is. Next-to-va-tel-but, the work of the current is equal.
Correct answer: 2.
33. B 15 No. 3522. What is the co-opposition of the electrical circuit between the points and, if each of the resistors has co-opposition?
Decision.
Since all the re-zi-sto-ry are the same, from the symmetry of the scheme for the key, that in ten-tsi-a-ly points and are equal, but it means that the current on the ver-ti-cal-noy pe-re-much-ke along the-to-well of Ohm, not on-te-even (since the on-line on it is equal to zero: ) and it can be thrown out of consideration and not taken into account when counting the general co-opposition (since what happened to her that without it, the current flows always the same). This fact can be understood in the following way. We pre-suppose that the current flows along the jumper downward, "over-re-top" the whole circuit around the go-to-zone-tal axis, the current in the re-moo-ke will now flow up, but the circuit itself has not changed, so the current in it should be the same as before pe-re-vo-ro-ta. The only va-ri-ant to satisfy this requirement, to-demand, so that the current in the pe-pipe was equal to zero.
Thus, we are moving towards a simpler scheme, its general co-opposition can be easily read by using the right la for after-to-va-tel-th and pa-ral-lel-no-th connection of conductors:.
If the co-oppos-le-nia would be different, then the ar-gu-men-you here would have lost the power and came to look for a common co-contraction of the first-in-the-first scheme, using the laws of Kirch-go-fa.
Correct answer: 4.
34. B 15 No. 3529.
Which of the inequalities is right to display the co-response between the powers, you-de-la-yu-shchi-mi-Xia on re-zi-hundred -rah; ; ; ?
Decision.
First, we note that the complete co-opposites of the upper and lower branches of the scheme are so-pa-da-yut:.
Left-to-va-tel-but, the current split-de-lit-Xia between these branches is exactly in-lam. In this way, one current flows through all the co-opposites. Power, you-de-la-yu-shcha-i-Xia on the re-zi-st-re, connected with the current strength, te-ku-shche-go through it and ve-li-chi with-against-against-le-tion with-from-but-she-ni.
On the other hand, the less co-oppo-le-tion, the less you-de-la-yu-shcha-i-Xia on it power. As-as-ku, for-key-cha-cha-what.
Correct answer: 3.
35. B 15 No. 3537.
Decision.
Determine de-lim sper-va full co-resistance of the load in the chain. The load represents a parall-lel-but co-unified re-zi-sto-ry and, to some, after-to-va- tel-but-connected re-zi-stor, next-to-va-tel-but, the total co-contra-lection of the load is equal. According to Ohm's law for a full circuit, the current strength is.
Correct answer: 2.
36. B 15 No. 3538.
The source of the current has an EMF, internal co-contra-lection,,. What is the strength of the current flowing through the source?
Decision.
Determine de-lim sper-va full co-resistance of the load in the chain. The load represents a parall-lel-but co-unified re-zis-sto-ry, and, next-to-va-tel-but, a common co- against-t-le-nie on-load-ki on-ho-dit-Xia following-du-yu-u-ra-zom:. According to Ohm's law for a full circuit, the current strength is.
Correct answer: 3.
37. B 15 No. 3587. On the rice-sun-ke, there is a diagram of an electrical circuit. Through which resistor does the largest current flow?
Decision.
The scheme represents a parallel co-unification of resistors No. 2, No. 3 and No. 4, to which after-to -two-tel-but-connected re-zi-store No. 1. With a subsequent connection, the current strength is one-on-one. With a parallel-lell-nn co-unity-ne-nii, the current strength is divided between the re-zi-sto-ra-mi in such a way that the power is drawn on all re -si-sto-rah was one-on-one. Left-to-va-tel-but, the max-si-mal-ny current flows through the res-zi-store No. 1.
The correct answer is: 1.
38. B 15 No. 3603. On the rice-sun-ke, there is a diagram of an electrical circuit. Through which resistor does the smallest current flow?
Decision.
The scheme represents a parallel co-unification of resistors No. 2 and No. 3, to which after-to-va- tel-but-keys-che-us of re-zi-stores No. 1 and No. 4. With a subsequent connection, the current strength is one-on-one. With a parallel-lell-nn co-unity-ne-nii, the current strength is divided between the re-zi-sto-ra-mi in such a way that the power is drawn on all re -si-sto-rah was one-on-one. Thus, one can immediately conclude that a greater current flows through the resistors No. 1 and No. 4 than through the resins-stations No. 2 and No. 3. According to Om's-to-well, on the re-zi-st-re connected with the current flowing through him with-from-but-she-ni:. And that means, for pa-ral-lel-but-connected res-ditch, we have:. Left-to-va-tel-but, a min-ni-mal-ny current flows through the resistor No. 3.
Correct answer: 3.
39. B 15 No. 3794. The co-contra-lection of each resistor in the circuit, as shown in the pic, is equal to 100 ohms. The study-stock is connected to the source in a hundred-yang-but-th-y-y-y-y-and-y. The power-supply on the resistor is equal to 12 V. The power-supply between the outputs of the circuit is equal to
Decision.
Re-zi-sto-ry, and connect-che-us after-to-va-tel-but. Left-to-va-tel-but, one-on-one current flows through them. Since their co-opposites are so-pa-da-yut, for-key, using Ohm's law for a section of the chain that is -nie on all these three resistors are the same and equal to 12 V. With a subsequent-to-final connection on-straight niya skla-dy-va-yut-Xia. So, to the section of the chain, including-cha-yu-shch-mu co-opp-le-niya, pr-lo-same-but-to-strand
But this is the direct connection between you-in-da-mi schemes.
Correct answer: 4.
40. B 15 No. 5365. AB
Decision.
The correct answer is indicated under number 2.
41. B 15 No. 5400. On the rice-sun-ke, there is a diagram of a section of an electrical circuit. By site AB a hundred-yang current is flowing A. What is the ideal-al-volt-meter, if it is opposed to Ohm?
Decision.
The ideal volt meter is on-line at the re-zi-st-re, which, according to Ohm, is equal to the Upper section of the chain and the lower -the section-drain of the circuit in the parallel section has one and the same co-opposite, that's why the current strength in these sections is the same -white and Then
The correct answer is indicated under number 3.
42. B 15 No. 6049.
Decision.
Let us assume that we are from-gi-ba-eat about the scheme, so that one of the above risks will be received. With such pre-ob-ra-zo-va-ni-yah we will get that the given scheme is eq-vi-va-tapes-on the diagram, indicated under number 3.
The correct answer is indicated under the number: 3.
43. B 15 No. 6084.
On the rice-sun-ke, there is a diagram of a section of an electrical circuit, one hundred and one of three re-zis-ditch R 1, R 2, R 3. On which of the following ri-sun-kov with-ve-de-on the electric-three-che-scheme of this section of the chain, eq-va-va-ribbon-naya given ?
Decision.
We assume that we are from-gi-ba-eat about the scheme, so that one of the above-given risks will be received. With such pre-ob-ra-zo-va-ni-yah, we will receive that the given scheme is eq-vi-va-tapes-on the diagram indicated under number 1.
The correct answer is indicated under the number: 1.
44. B 15 No. 6342. From the pro-in-lo-ki, in a hundred-yang-no-go-th-c, I made a square-frame frame. To the point AND under-connected pro-water. To which of the numbered points of the frame should be connected to another wire, so that the co-contra was the new section of the chain max-si-mal-ny?
Decision.
Co-opposition between the point AND and other-gi-mi point-ka-mi calculate-
When solving problems on a mixed connection of conductors, it is necessary to try to transform the circuit and replace the parallel and series-connected conductors with equivalent conductors.
In the given example, it should be borne in mind that the first and second conductors cannot be considered connected in series, since there is a branch at the point of their connection. For the same reason, conductors 1–3 and 4–5 cannot be considered connected in series.
Conductor 1 and conductor 2,3 are connected in series. They can also be replaced with one equivalent conductor, the resistance of which is equal to the sum of the resistances of conductors 1 and 2.3. Having found this resistance, we draw the transformed circuit again. In this circuit, the conductor 1,2,3 is connected in parallel with the conductor 5. The resistance of the parallel-connected conductors can also be calculated using the well-known formula and replaced with one conductor with an equivalent resistance of 1,2,3,5.
For example, if we were dealing with four conductors connected as shown in the diagram, the problem would be solved elementary. Pairs of conductors 1,2 and 3,4 are connected in series. They can be replaced with equivalent conductors. These equivalent conductors are connected in parallel and are also easy to replace with one common conductor. (If the resistances of the conductors were 10 ohms each, then the total resistance of the circuit would also be 10 ohms).
Let a current flow into point A with a force I 0. At this point, the current forks. Part of it flows through the top of the chain, part through the bottom. It may happen that the current that flows in the upper and lower sections is the same.
In problems of calculating electrical circuits, it is useful to draw an analogy between an electric current and the current of water in pipes. Let's try to mentally carry out such a replacement in the problem under consideration.
Let, for simplicity, pipes 1, 2, 3, 4 are the same in cross section and length. The same currents flow along two parallel branches. Further, the pipes converge into one pipe. It is obvious that the incoming current is equal to the outgoing current. If you put an isthmus connecting two pipelines, then in this isthmus, due to the equality of the pressures on both sides, water will not flow in either direction, whatever the isthmus. This isthmus may well be excluded from consideration of the process.
So it is in electrical circuits. If it turns out that the potentials of points C and D are equal to each other, then there will be no current through conductor 5.
Thus, when we come to a fundamentally non-transformable electrical circuit, we must try to find points with equal potentials in this circuit. If this can be done, then any conductor connecting these points can be excluded from the circuit. Also, points with equal potentials can be connected to each other by any conductor, including those with zero resistance.
In this case, the potentials of points C and D will be equal if the resistances of the conductors 1–4 are equal.
The resistances of conductors 1 and 3, 2 and 4 can be equal. All the same, the currents in the upper and lower branches will be equal to each other. The voltage drops on conductors 1 and 3, 2 and 4 will also be equal to each other, so there will be no current in the resistor 5 circuit. Due to this, resistor 5, at any of its resistance, can be discarded from consideration.
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However, it may turn out that the potentials of points C and D are not equal to each other. Then the flow of currents I 1 and I 3 should be considered further. Let's assume that the current is I 1\u003e I 3. I 1 reaches point C, and branches further. Part of the current goes through resistor 2, and part through resistor 5. Currents I 4 and I 3 converge at point D. These currents go further through resistor 4, so the current I 5 is equal to the sum of currents I 4 and I 3. The current I 5 will merge with the current I 2 and form a current equal to the original current I 0.
Thus, we conclude the following.
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Further in the chain, you need to select closed contours. For this, an arbitrary point is taken and movement along the chain begins so as to return to this point. When walking, you must adhere to one direction. The number of contours should be such that it is possible to bypass all the elements of the chain.
If there are no current sources in the circuit, then the sum of the voltage drops is zero. Let's go around elements 1-5-3, moving clockwise.
The resulting system of equations can be solved for unknown quantities.
Dependence of power and efficiency of the current source on the load
Devices and accessories:laboratory panel, two batteries, milliammeter, voltmeter, variable resistors.
Introduction. The most widespread sources of direct current are galvanic cells, batteries, rectifiers. We connect to the current source that part that needs its electrical energy (light bulb, radio receiver, calculator, etc.). This part of the electrical circuit is called a common word - load. The load has some electrical resistance R and consumes a current from the source I (fig. 1).
The load forms the outer part of the electrical circuit. But there is also an inner part of the circuit - this is actually the current source itself, it has electrical resistance r, the same current flows in it I. The boundary between the internal and external sections of the circuit is the terminals "+" and "-" of the current source to which the consumer is connected
In Figure 1, the current source is enclosed by a dashed outline.
Power supply with electromotive force E creates a current in a closed circuit, the strength of which is determined ohm's law:
When current flows through resistances R and r heat energy is released in them, determined by law Joule-Lenz.Power in the outside of the circuit R e - external power
This power is useful.
Internal power R i - internal power... It is not available for use and therefore amounts to lossespower source
Full power source power R is the sum of these two terms,
As can be seen from the definitions (2,3,4), each of the powers depends both on the flowing current and on the resistance of the corresponding part of the circuit. Let's consider this dependence separately.
Power dependenceP e , P i , P from the load current.
Taking into account Ohm's law (1), the total power can be written as follows:
In this way, apparent power of the source is directly proportional to consumed current.
The power allocated to 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 valid for an open circuit when R , the second corresponds to the so-called short circuit source when the resistance of the external circuit R = 0 ... In this case, the current in the circuit (see formula (1)) reaches the highest value - short-circuit current.
At this current complete power becomes greatest
R nb = EI kz \u003d E 2 / r. (9)
However, all of it stands out inside source.
Let us find out under what conditions the external power becomes maximum... Power dependence P e from the current is (see formula (6)) parabolic:
.
The position of the maximum of the function is determined from the condition:
dP e / dI \u003d 0, dP e / dI \u003d E - 2Ir.
Useful power reaches its maximum value at current
which is half the short-circuit current (8), (see Fig. 2):
The external power at this current is
(12)
those. the maximum external power is one fourth of the maximum apparent power of the source.
Power released on the internal resistance at current I max is defined as follows:
,
(13)
those. is also one quarter of the maximum total power of the current source. Note that at a current I max
P e = P i . (14)
When the current in the circuit tends to the highest value I kz , internal power
those. equal to the maximum power of the source (9). This means that all the power of the source is allocated to its internal resistance, which, of course, is harmful from the point of view of the safety of the current source.
Characteristic points of the dependence graph P e = P e (I) are shown in Fig. 2.
Efficiency operation of the current source is estimated by its efficiency... The efficiency is the ratio of the useful power to the total power of the source:
= P e / P.
Using formula (6), the expression for the efficiency can be written as follows:
.
(15)
From formula (1) it is seen that E – Ir = IR there is tension U on external resistance. Therefore, the efficiency
= U/ E . (16)
It also follows from expression (15) that
= (17)
those. The efficiency of the source depends on the current in the circuit and tends to the largest value equal to unity at a current I 0 (fig. 3) . With an increase in the current strength, the efficiency decreases linearly and becomes zero during a short circuit, when the current in the circuit becomes the highest I kz = E/ r .
From the parabolic nature of the dependence of external power on current (6) it follows that the same power at the load P e can be obtained at two different values \u200b\u200bof the current in the circuit. From the formula (17) and from the graph (Fig. 3) it can be seen that in order to obtain a higher efficiency from the source, it is preferable to work at lower load currents, where this coefficient is higher.
2.Power dependenceP e , P i , P from load resistance.
Consider dependence complete, useful and internal power from external resistanceR in the source circuit with EMF E and internal resistance r.
Full the power developed by the source can be written as follows, if the expression for current (1) is substituted into formula (5):
So the total power depends on the load resistance R. It is greatest at a short circuit of the circuit, when the load resistance becomes zero (9). With increasing load resistance R the total power decreases, tending to zero at R .
On external resistance stands out
(19)
External power R e is part of the total power R and its value depends on the ratio of resistances R/(R+ r) ... When short-circuited, the external power is zero. With increasing resistance R it increases first. When R r external power tends to full in size. But the useful power itself becomes small in this case, since the total power decreases (see formula 18). When R external power tends to zero as well as total power.
What should be the load resistance to get from a given source maximum external (useful) power (19)?
Let's find the maximum of this function from the condition:
Solving this equation, we get R max \u003d r.
In this way, in the external circuit, the maximum power is released if its resistance is equal to the internal resistance of the current source. Under this condition, the current in the circuit is E/2 r, those. half the short-circuit current (8). Maximum net power at this resistance
(21)
which coincides with what was obtained above (12).
Power released on the internal resistance of the source
(22)
When R P i Pand at R=0 reaches the highest value P i nb = P nb = E 2 / r... When R= r internal power is half full, P i = P/2 ... When R r it decreases in almost the same way as the full one (18).
The dependence of efficiency on the resistance of the external part of the circuit is expressed as follows:
=
(23)
It follows from the obtained formula that the efficiency tends to zero as the load resistance approaches zero, and the efficiency tends to the largest value equal to unity as the load resistance increases to R r ... But the useful power decreases almost as 1/ R (see formula 19).
Power R e reaches its maximum value at R max = r, The efficiency in this case is equal, according to formula (23), = r/(r+ r) = 1/2. In this way, the condition for obtaining the maximum useful power does not coincide with the condition for obtaining the highest efficiency.
The most important result of this consideration is the optimal matching of the source parameters with the nature of the load. Three areas can be distinguished here: 1) R r, 2)R r, 3) R r. First the case takes place where a low power is required from a source for a long time, for example, in an electronic clock, microcalculators. The dimensions of such sources are small, the supply of electrical energy in them is small, it must be consumed sparingly, so they must work with high efficiency.
Second case - a short circuit in the load, in which all the power of the source is released in it and the wires connecting the source to the load. This leads to excessive heating and is a fairly common cause of fires and fires. Therefore, a short circuit of high power current sources (dynamos, batteries, rectifiers) is extremely dangerous.
IN third case, they want to get maximum power from the source at least a short time, for example, when starting a car engine with an electric starter, the efficiency is not so important. The starter is switched on for a short time. Long-term operation of the source in this mode is practically unacceptable, since it leads to a rapid discharge of the car battery, its overheating and other troubles.
To ensure the operation of chemical current sources in the desired mode, they are connected together in a certain way into the so-called batteries. Cells in a battery can be connected in series, in parallel, and in a mixed circuit. This or that connection scheme is determined by the load resistance and the amount of current consumed.
The most important operational requirement for power plants is their high efficiency. From formula (23) it can be seen that the efficiency tends to unity if the internal resistance of the current source is small compared to the load resistance
In parallel, you can connect elements that have the same EMF. If connected n identical elements, then from such a battery you can get a current
Here r 1 - resistance of one element, E 1 - EMF of one element.
It is advantageous to use such a connection at a low-impedance load, i.e. at R r. Since the total internal resistance of the battery in parallel connection decreases by n times in comparison with the resistance of one element, then it can be made close to the resistance of the load. This increases the efficiency of the source. Increases in n times and the energy capacity of the battery of cells.
r, then it is more profitable to connect the elements in a battery in series. In this case, the EMF of the battery will be in n times more EMF of one element and the required current can be obtained from the sourceThe purposeof this laboratory work is experimental verification the theoretical results obtained above on the dependence of the total, internal and external (useful) power and the efficiency of the source both on the strength of the consumed current and on the load resistance.
Description of the installation. To study the performance characteristics of the current source, an electrical circuit is used, the diagram of which is shown in Fig. 4. Two alkaline batteries NKN-45 are used as a current source, which are connected successively in one battery through a resistor r , which simulates the internal resistance of the source.
Its inclusion artificially increases the internal resistance of accumulators, which 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 will of the experimenter. As a load (external resistance of the circuit) n 
two variable resistors are used R 1
and R 2
... (one coarse adjustment, the other fine), which provides smooth current regulation in a wide range.
All instruments are mounted on a laboratory panel. The resistors are fixed under the panel, their control knobs and terminals are brought up, near which there are corresponding inscriptions.
Measurements. 1.Set the switch Pto neutral position, switch VCopen. Turn the knobs of the resistors counterclockwise until they stop (this corresponds to the greatest load resistance).
Collect electrical circuit according to the scheme (Fig. 4), not while attaching current sources.
After checking the assembled circuit by a teacher or laboratory assistant, connect the batteries E 1 and E 2 respecting the polarity.
Set the short-circuit current. To do this, put the switch P to position 2 (external resistance is zero) and using a resistor r set the arrow of the milliammeter to the maximum (rightmost) division of the instrument scale - 75 or 150 mA. Thanks to the resistor r the laboratory setup has ability to regulate internal resistance of the current source. In fact, internal resistance is a constant value for of this type sources and cannot be changed.
Put the switch P into position 1 , thus turning on the external resistance (load) R= R 1 + R 2 into the source chain.
Changing the current in the circuit through 5 ... 10 mA from the highest to the lowest value using resistors R 1 and R 2 , write down the milliammeter and voltmeter readings (voltage across the load U) into the table.
Put the switch P to the neutral position. In this case, only a voltmeter is connected to the current source, which has a rather high resistance compared to the internal resistance of the source, so the voltmeter reading will be slightly less than the EMF source. Since you have no other way to determine its exact value, it remains to take the voltmeter reading for E... (For more on this, see laboratory work No. 311).
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Processing results... 1. For each current value, calculate:
full power according to the formula (5),
external (useful) power according to the formula,
internal power from the ratio
resistance of the external section of the circuit from Ohm's law R= U/ I,
The efficiency of the current source according to the formula (16).
Plot dependency graphs:
total, useful and internal power from current I (on one tablet),
total, useful and internal power from resistance R (also on one tablet); it is wiser to build only a part of the graph corresponding to its low-resistance part, and discard 4-5 experimental points out of 15 in the high-resistance region,
Source efficiency versus current consumption I,
Efficiency from load resistance R.
From charts P e from I and P e from R determine the maximum net power in the external circuit P e max.
From the graph 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 efficiency of the current source at I max and at R max .
test questions
1. Draw a diagram of the electrical circuit used in the work.
2.What is the current source? What is the load? What is the inner section of the chain? Where does the outer section of the chain begin and where does it end? Why is the variable resistor installed? r ?
3. What is called external, useful, internal, total power? What is the power loss?
4. Why the useful power in this work is proposed to be calculated by the formula P e = IU, and not by formula (2)? Justify these recommendations.
5. Compare the experimental results obtained by you with the calculated ones given in the methodological manual, both when studying the dependence of power on current and on load resistance.
Sources currentAbstract \u003e\u003e Physics
Continues from 3 to 30 min in dependencies from temperature ... power (up to 1.2 kW / kg). The discharge time does not exceed 15 minutes. 2.2. Ampoule sources current ... to smooth out vibrations load in power systems in ... a relatively low Efficiency (40-45%) and ...
Capacities harmonic oscillations in electrical circuits
Lecture \u003e\u003e Physics... from source in load necessary average power... Since the complex stresses and currents ... load and developed by the generator power, is equal to \u003d 0.5. With increasing RH - average power decreases but increases Efficiency... Schedule dependencies Efficiency ...
... power devices - consumed power devices - output power devices - Efficiency Devices Accept Efficiency ... which in dependencies from depth of regulation ... constant independently from changes current load... Have sources power supply with ...
... power UPS are divided into Sources uninterruptible power supply small power (with full power ... from accumulators, minus - decrease Efficiency ... current compared to the nominal value current load... ... 115 V dependencies from load; Attractive appearance ...
