{"id":11332,"date":"2024-11-08T16:26:07","date_gmt":"2024-11-08T16:26:07","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11332"},"modified":"2024-12-03T13:07:28","modified_gmt":"2024-12-03T13:07:28","slug":"resistor-equivalente-2","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrodinamica\/resistor-equivalente-2\/","title":{"rendered":"EN equivalent resistor"},"content":{"rendered":"

EQUIVALENT RESISTOR<\/h1>\n
\n

\u00a0Equivalent resistor<\/b><\/p>\n

<\/b>Equivalent\u00a0<\/b>resistor (\u00a0<\/b>Req<\/b><\/sub>\u00a0)\u00a0<\/b>Many times you need to\u00a0<\/b>replace a resistor of a certain\u00a0<\/b>nominal value in an electrical circuit, but you don’t have it.<\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/p>\n

However, you can\u00a0<\/b>replace it with an association of resistors that has the same\u00a0<\/b>nominal value.\u00a0<\/b>This\u00a0<\/b>association\u00a0<\/b>is called the\u00a0\u00a0<\/b>equivalent resistor (Req\u00a0<\/b>)<\/b><\/sub>\u00a0of\u00a0<\/b>the association,\u00a0<\/b>which is\u00a0<\/b>the one that, subjected to the same potential difference as the association, is traversed by the same current, without altering the characteristics of the circuit.<\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0<\/b><\/b><\/b><\/p>\n

Equivalent resistor in series association<\/b><\/p>\n

A \u00a0\u00a0<\/b>series association\u00a0<\/b>\u00a0is one in which\u00a0<\/b>resistors are associated one after the other so that the current in each is the same.<\/b><\/p>\n

\"\"<\/p>\n

Calculation of the resistance (R\u00a0<\/b>eq<\/b><\/sub>\u00a0) of the equivalent resistor\u00a0<\/b>in the series association\u00a0<\/b>the \u00a0\u00a0<\/b>resistance\u00a0<\/b>of the\u00a0<\/b>equivalent resistor between A and B\u00a0<\/b>is given by the\u00a0<\/b>sum of the resistances of each resistor.<\/b>\u00a0<\/b><\/b>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Numerical examples:<\/b><\/p>\n

\"\"<\/p>\n

Equivalent resistor in parallel association<\/b><\/p>\n

<\/b>Parallel association\u00a0<\/b>is\u00a0<\/b>\u00a0one in which\u00a0\u00a0<\/b>the\u00a0<\/b>resistors are associated by their terminals\u00a0<\/b>, that is,\u00a0<\/b>they all leave from the same point (A) and all arrive at the same point (B).<\/b><\/p>\n

\"\"<\/p>\n

Calculation of the resistance (R\u00a0<\/b>eq<\/b><\/sub>\u00a0) of the equivalent resistor in parallel association:<\/b><\/p>\n

Three processes:<\/b><\/p>\n

\"\"<\/p>\n

3rd\u00a0<\/b>\u2013<\/b><\/sup>\u00a0\u00a0Practical rule\u00a0<\/b>\u00a0:<\/b><\/b><\/p>\n

\"\"\u00a0when\u00a0<\/b>one\u00a0<\/b>is\u00a0<\/b>twice\u00a0<\/b>the other, you\u00a0<\/b>take the larger one and divide it by three;<\/b><\/p>\n

when\u00a0<\/b>one\u00a0<\/b>is\u00a0<\/b>three times\u00a0<\/b>the other, you\u00a0<\/b>take the larger one and divide it by four,\u00a0<\/b>and so on.<\/b><\/p>\n

\"\"\u00a0two equal resistors\u00a0<\/b>, you\u00a0<\/b>divide the value of one of them by two;<\/b><\/p>\n

three equal resistors\u00a0<\/b>, you\u00a0<\/b>divide the value of one of them by three,\u00a0<\/b>and so on.\u00a0<\/b><\/p>\n

In some cases this rule of thumb, when the\u00a0<\/b>number is not exact\u00a0<\/b>,\u00a0<\/b>can be replaced\u00a0<\/b>by\u00a0<\/b>one of the two above.<\/b><\/p>\n

Numerical example:<\/b><\/p>\n

\"\"<\/p>\n

1st\u00a0<\/b>process<\/b><\/sup>\u00a0\u00a0:<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

If you reversed the order, the result would be the same:<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Equivalent resistor in mixed combination<\/b><\/p>\n

\u00a0Mixed Association\u00a0<\/b>consists of a\u00a0<\/b>combination of series and parallel associations,\u00a0<\/b>which you must calculate\u00a0<\/b>in parts until you reach a single equivalent resistor R\u00a0<\/b>eq<\/b><\/sub>\u00a0.<\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

To do this, you must\u00a0<\/b>replace each partial association, series or parallel\u00a0<\/b>, with a\u00a0<\/b>single resistor\u00a0<\/b>and\u00a0<\/b>gradually\u00a0<\/b>reduce the\u00a0<\/b>association scheme.<\/b><\/b><\/b><\/p>\n

Analyze these examples in detail:<\/b><\/b><\/p>\n

In\u00a0<\/b>each case\u00a0<\/b>below, calculate the\u00a0<\/b>equivalent resistance between points P and Q.<\/b><\/p>\n

01-<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

02-<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

 <\/p>\n

03-\u00a0<\/b>Look, the last three are in series,\u00a0<\/b>start with them:<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Want to\u00a0<\/b>learn more?\u00a0<\/b>See exercises\u00a0<\/b>01 (d, e, i, jel); 06; 13 and 33 with their respective solutions.<\/b><\/p>\n

What you should know, information and tips<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Calculation of the resistance (R\u00a0<\/b>eq<\/b><\/sub>\u00a0) of the equivalent resistor in parallel association:<\/b><\/p>\n

Three processes:<\/b><\/p>\n

\"\"<\/p>\n

3rd\u00a0<\/b>\u2013<\/b><\/sup>\u00a0\u00a0Practical rule\u00a0<\/b>\u00a0:<\/b><\/b><\/p>\n

\"\"\u00a0when\u00a0<\/b>one\u00a0<\/b>is\u00a0<\/b>twice\u00a0<\/b>the other, you\u00a0<\/b>take the larger one and divide it by three;<\/b><\/p>\n

when\u00a0<\/b>one\u00a0<\/b>is\u00a0<\/b>three times\u00a0<\/b>the other, you\u00a0<\/b>take the larger one and divide it by four,\u00a0<\/b>and so on.<\/b><\/p>\n

\"\"\u00a0two equal resistors\u00a0<\/b>, you\u00a0<\/b>divide the value of one of them by two;<\/b><\/p>\n

three equal resistors\u00a0<\/b>, you\u00a0<\/b>divide the value of one of them by three,\u00a0<\/b>and so on.\u00a0<\/b><\/p>\n

In some cases this rule of thumb, when the\u00a0<\/b>number is not exact\u00a0<\/b>,\u00a0<\/b>can be replaced\u00a0<\/b>by\u00a0<\/b>one of the two above.<\/b><\/p>\n

\"\"<\/p>\n

The\u00a0<\/b>\u00a0lower\u00a0<\/b>\u00a0the equivalent resistance\u00a0<\/b>of a resistor association,\u00a0\u00a0<\/b>the greater\u00a0<\/b>\u00a0the power\u00a0<\/b>dissipated by it, so that its efficiency is greater.\u00a0<\/b>\u00a0Justification\u00a0\u00a0<\/b>P\u00a0<\/b>o<\/b><\/sub>\u00a0= U\u00a0<\/b>2<\/b><\/sup>\u00a0\/R\u00a0<\/b>eq<\/b><\/sub>\u00a0\u00a0 Note that the\u00a0<\/b>power is inversely proportional to the equivalent resistance.<\/b>\u00a0<\/b><\/b>\u00a0\u00a0\"\"\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/p>\n

\"\"\u00a0Circuit breakers<\/b><\/p>\n

Circuit breakers\u00a0<\/b>The function of the\u00a0<\/b>circuit breaker is to automatically interrupt the passage of\u00a0<\/b>electrical current through one of the points (rooms) of the residence\u00a0<\/b>, when its\u00a0<\/b>intensity exceeds a certain\u00a0<\/b>value\u00a0<\/b>(the switch turns off).<\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

If the\u00a0<\/b>circuit breaker switch did not turn off due to the excess electrical current\u00a0<\/b>, the\u00a0<\/b>circuit wires would become very hot and could melt, causing fires.<\/b><\/p>\n

\"\"<\/p>\n

Next to the circuit breakers,\u00a0<\/b>in the electrical box, there is a\u00a0<\/b>panel identifying the rooms or points served by each circuit breaker, such as lighting, sockets, showers, etc.<\/b><\/p>\n

\"\"<\/p>\n

Rheostats<\/b><\/p>\n

Rheostats\u00a0<\/b>are variable resistors\u00a0<\/b>whose purpose is\u00a0<\/b>to adapt the intensity of the electric current to desired values.<\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b><\/p>\n

Types of rheostats:<\/b><\/p>\n

The\u00a0<\/b>main types of rheostats are\u00a0<\/b>cursor rheostat\u00a0<\/b>varying the cursor\u00a0<\/b>you are<\/b>\u00a0<\/b><\/b>\u00a0<\/b>\u00a0\"\"<\/b>\u00a0\u00a0<\/b><\/b>\u00a0\"\"<\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b><\/p>\n

\"\"varying the resistance\u00a0<\/b>(figure 1) \u00a0\u00a0<\/b>point\u00a0\u00a0<\/b>rheostat\u00a0<\/b>in\u00a0<\/b>each position of the switch\u00a0<\/b>the\u00a0<\/b>electrical resistance\u00a0<\/b>has\u00a0<\/b>a\u00a0<\/b>certain value\u00a0<\/b>(figure 2).<\/b>\u00a0<\/b>\"\"\u00a0<\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b><\/b>\u00a0\"\"<\/b><\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b><\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b>\u00a0<\/b><\/b><\/p>\n

Short circuit (DC)<\/b><\/p>\n

 <\/p>\n

When\u00a0<\/b>two points of an electrical circuit are connected (joined) by a conductor (wire) of\u00a0<\/b>negligible resistance (ideal wire, wire without resistance),\u00a0<\/b>these two points are said\u00a0<\/b>to be in a short circuit (CC).<\/b><\/b><\/b><\/b><\/b><\/p>\n

Consider a\u00a0<\/b>resistor R\u00a0<\/b>being traversed by an\u00a0<\/b>electric current\u00a0<\/b>ie subjected to a\u00a0<\/b>potential difference U\u00a0<\/b>AB<\/b><\/sub>\u00a0= V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0\u2013 V\u00a0<\/b>B.<\/b><\/sub><\/p>\n

\"\"<\/p>\n

By connecting,\u00a0<\/b>in parallel, between points A and B of this resistor\u00a0<\/b>, a\u00a0<\/b>conductor of negligible resistance (ideal wire),\u00a0<\/b>a short circuit is caused\u00a0<\/b>between A and B\u00a0<\/b>and it is verified that\u00a0<\/b>all the electric current will be diverted, passing through the ideal wire\u00a0<\/b>, in which,\u00a0<\/b>applying Ohm’s law, we will have\u00a0<\/b>\u00a0 V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0– V\u00a0<\/b>B<\/b><\/sub>\u00a0= U\u00a0<\/b>AB<\/b><\/sub>\u00a0= Ri\u00a0\u00a0<\/b>\u00a0 as\u00a0<\/b>R = 0 (ideal wire),\u00a0<\/b>we have\u00a0\u00a0<\/b>V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0– V\u00a0<\/b>B<\/b><\/sub>\u00a0= Ri\u00a0<\/b>\u00a0 V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0– V\u00a0<\/b>B<\/b><\/sub>\u00a0= 0.i\u00a0\u00a0<\/b>\u00a0 V\u00a0<\/b>A<\/b><\/sub>\u00a0\u00a0– V\u00a0<\/b>B<\/b><\/sub>\u00a0= 0\u00a0\u00a0<\/b>V\u00a0<\/b>A<\/b><\/sub>\u00a0= V\u00a0<\/b>B.<\/b><\/sub>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b>\"\"<\/b><\/b><\/b><\/b>\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/p>\n

Thus, the\u00a0<\/b>circuit behaves as if the resistor did not exist\u00a0<\/b>and the circuit can be\u00a0<\/b>redesigned, making points A and B coincident.<\/b><\/p>\n

Examples of calculating the resistance value (R\u00a0<\/b>eq)<\/b><\/sub>\u00a0of the equivalent resistor,\u00a0<\/b>with short circuit (CC)<\/b><\/p>\n

Calculate,\u00a0<\/b>in each case, the\u00a0<\/b>resistance of the equivalent resistor between points A and B:<\/b><\/p>\n

the)<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

b)<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

w)<\/b><\/p>\n

\"\"<\/p>\n

 <\/p>\n

 <\/p>\n

Calculation of the equivalent resistor in more complex short-circuit cases<\/b><\/p>\n

\u00a0In\u00a0<\/b>some more complex short-circuit cases\u00a0<\/b>,\u00a0<\/b>it is not possible to visualize the situation (the short-circuited points)\u00a0<\/b>and it is necessary\u00a0<\/b>to redo the circuit\u00a0<\/b>, proceeding in the following\u00a0<\/b>practical manner:<\/b><\/p>\n

1st\u00a0<\/b>Mark<\/b><\/sup>\u00a0all the\u00a0<\/b>nodes\u00a0<\/b>of the association\u00a0<\/b>(node \u200b\u200b\u2013 crossing point of 3 or more wires)\u00a0<\/b>.<\/b>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

2.\u00a0<\/b>Place<\/b><\/sup>\u00a0letters\u00a0<\/b>on\u00a0<\/b>each node,\u00a0<\/b>remembering that the\u00a0<\/b>points joined by an ideal wire (nodes)\u00a0<\/b>are in a\u00a0<\/b>short circuit and must be named with the same letter\u00a0<\/b>, as they have the\u00a0<\/b>same\u00a0<\/b>potential.<\/b>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

3.\u00a0<\/b>Redo<\/b><\/sup>\u00a0the circuit<\/b>\u00a0\"\"<\/b><\/b><\/p>\n

 <\/p>\n

Examples of calculating the resistance value (R\u00a0<\/b>eq)<\/b><\/sub>\u00a0of the equivalent resistor,\u00a0<\/b>with short circuit (CC), redoing the circuit<\/b><\/p>\n

Determine, in\u00a0<\/b>each case\u00a0<\/b>,\u00a0<\/b>between\u00a0<\/b>points\u00a0<\/b>P and Q,\u00a0<\/b>the\u00a0<\/b>equivalent resistance\u00a0<\/b>of each association:<\/b><\/p>\n

the)<\/b><\/p>\n

\"\"<\/p>\n

Steps:\u00a0<\/b>Pay close attention to the steps of the resolution.<\/b><\/p>\n

\"\"<\/p>\n

\"\"\u00a0Remaking the circuit<\/b><\/p>\n

The resistors between points P and P\u00a0<\/b>, joined by the\u00a0<\/b>same letter, are in short circuit.\u00a0<\/b>Do not place the\u00a0<\/b>5\u03a9 and 30\u03a9\u00a0<\/b>resistors\u00a0<\/b>\u00a0 between\u00a0<\/b>P and B. There\u00a0<\/b>is\u00a0<\/b>one\u00a0<\/b>of 30\u03a9\u00a0<\/b>and one\u00a0<\/b>of 8\u03a9\u00a0<\/b>between B and Q.<\/b>\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

one\u00a0<\/b>of 10\u03a9\u00a0<\/b>\u00a0 see diagram and sequence above.<\/b>\u00a0\u00a0\"\"<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

w)<\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Note:\u00a0<\/b>If you want\u00a0<\/b>to go deeper\u00a0<\/b>, analyze exercises 26; 28(c); 29; 30; 34(c) and 35, with their respective solutions.<\/b><\/p>\n

Check out the exercises with commented solutions<\/a><\/h3>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

EQUIVALENT RESISTOR \u00a0Equivalent resistor Equivalent\u00a0resistor (\u00a0Req\u00a0)\u00a0Many times you need to\u00a0replace a resistor of a certain\u00a0nominal value in an electrical circuit, but you don’t have it.\u00a0\u00a0 However, you can\u00a0replace it with an association of resistors that has the same\u00a0nominal value.\u00a0This\u00a0association\u00a0is called the\u00a0\u00a0equivalent resistor (Req\u00a0)\u00a0of\u00a0the association,\u00a0which is\u00a0the one that, subjected to the same potential difference as the association, is traversed by the<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1676,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-11332","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=11332"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11332\/revisions"}],"predecessor-version":[{"id":12015,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11332\/revisions\/12015"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1676"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=11332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}