{"id":11312,"date":"2024-11-08T12:44:31","date_gmt":"2024-11-08T12:44:31","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11312"},"modified":"2024-12-03T13:03:43","modified_gmt":"2024-12-03T13:03:43","slug":"lei-de-pouillet-receptores-en","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/eletricidade\/eletrodinamica\/lei-de-pouillet-receptores-en\/","title":{"rendered":"Pouillet’s Law – EN Receptors"},"content":{"rendered":"

POUILLET’S LAW \u2013 RECEPTORS<\/span><\/h1>\n
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Receivers \u2013 Association of generators with receivers \u2013 Pouillet\u2019s Law<\/span><\/b><\/p>\n

Electrical receiver<\/span><\/b><\/p>\n

<\/a><\/p>\n

A\u00a0<\/span><\/b>device\u00a0<\/span><\/b>that\u00a0<\/span><\/b>converts electrical energy into another form of energy, not exclusively thermal. Examples:\u00a0<\/span><\/b>electric motors, fans, blenders, refrigerators, stereos, videos, cell phones, computers, etc.<\/b><\/span><\/b><\/b><\/p>\n

\"\"<\/p>\n

A\u00a0<\/span><\/b>fan, for example\u00a0<\/span><\/b>,\u00a0<\/span><\/b>converts thermal energy into mechanical energy;\u00a0<\/span><\/b>this\u00a0<\/span><\/b>conversion,\u00a0<\/span><\/b>however,\u00a0<\/span><\/b>is not complete,\u00a0<\/span><\/b>as\u00a0<\/span><\/b>part of the energy is inevitably converted into thermal energy.<\/span><\/b><\/p>\n

Characteristic quantities of an electrical receiver<\/span><\/b><\/p>\n

There\u00a0<\/span><\/b>are two:\u00a0<\/span><\/b>the\u00a0<\/span><\/b>first\u00a0<\/span><\/b>is the\u00a0<\/span><\/b>counter-electromotive force (E’),\u00a0<\/span><\/b>a quantity (\u00a0<\/span><\/b>measured\u00a0<\/span><\/b>in\u00a0<\/span><\/b>volts \u201c1V=1J\/C\u201d\u00a0<\/span><\/b>)\u00a0<\/span><\/b>defined\u00a0<\/span><\/b>as the\u00a0<\/span><\/b>ratio between the work (W) and the amount of charge (Q) that performs this work inside\u00a0<\/span><\/b>the\u00a0<\/span><\/b>receiver and which is the potential difference actually used to produce non-thermal energy; the second is its internal resistance r’.<\/span><\/b><\/p>\n

Schematic representation of a receiver<\/span><\/b><\/p>\n

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Electrical circuit with a generator powering a receiver<\/span><\/b><\/p>\n

\u00a0In the\u00a0<\/span><\/b>circuit shown in the figure, a generator (battery)\u00a0<\/span><\/b>powers a receiver (motor),\u00a0<\/b>establishing a\u00a0<\/b>potential difference across it.<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

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Receiver equation<\/span><\/b><\/p>\n

Consider an\u00a0<\/span><\/b>electrical receiver\u00a0<\/span><\/b>(a small electric fan, for example), receiving\u00a0<\/span><\/b>U = 2 V from a\u00a0<\/span><\/b>battery\u00a0<\/b>(meaning that the motor receives 2J of electrical energy from the battery for every 1C of charge that passes through it).<\/b><\/span><\/b><\/b><\/b><\/p>\n

Suppose that U’ = r’.i = 0.5V\u00a0<\/span><\/b>(meaning that a portion of electrical energy equal to 0.5J received by the fan, for each 1C of charge that passes through it, is\u00a0<\/span><\/b>converted into thermal energy\u00a0<\/span><\/b>,\u00a0<\/span><\/b>needlessly heating the motor (energy dissipated, lost, wasted).<\/span><\/b><\/p>\n

For the\u00a0<\/span><\/b>motor (receiver) to produce mechanical energy\u00a0<\/span><\/b>,\u00a0<\/span><\/b>there remains\u00a0\u00a0<\/span><\/b>E’ = U \u2013 r’.i =\u00a0<\/b>2 \u2013 0.5\u00a0\u00a0<\/b>E’ = 1.5V, which means\u00a0<\/b>that an\u00a0<\/b>electrical energy of 1.5J is usefully converted into non-thermal energy (mechanical, in this case), for each 1C of charge that passes through the motor (receiver).<\/b><\/span>\u00a0\"\"\u00a0\u00a0<\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/p>\n

Like this:<\/span><\/b><\/p>\n

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Receiver characteristic curve<\/span><\/b><\/p>\n

\u00a0\"\"<\/p>\n

Powers of a receiver (equations)<\/span><\/b><\/p>\n

\"\"\u00a0\u00a0Total power (P\u00a0<\/span><\/b>t<\/span><\/b><\/sub>\u00a0)\u00a0<\/span><\/b>corresponds to the total energy received by the receiver from the external source (generator) per unit of time:<\/b><\/span>\u00a0\"\"<\/b><\/b><\/p>\n

\"\"<\/p>\n

\"\"\u00a0Dissipated power (P\u00a0<\/span><\/b>d<\/span><\/b><\/sub>\u00a0)\u00a0<\/span><\/b>refers to the\u00a0<\/b>power consumed\u00a0<\/b>(\u201clost\u201d, dissipated, in thermal form) by the\u00a0<\/b>internal resistance r’\u00a0<\/b>of the receiver and provided by:<\/b><\/span>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/p>\n

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\"\"\u00a0Useful power (P\u00a0<\/span><\/b>u<\/span><\/b><\/sub>\u00a0)\u00a0<\/span><\/b>power used by the receiver\u00a0<\/b>for its\u00a0<\/b>normal operation,\u00a0<\/b>in\u00a0<\/b>non-thermal form\u00a0<\/b>.<\/b><\/span>\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Example:\u00a0<\/span><\/b>in a\u00a0<\/span><\/b>fan, it is the portion of the total energy that is transformed into exclusively mechanical energy, to turn its blades.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Efficiency (\u03b7) of a receiver<\/span><\/b>\u00a0<\/b><\/p>\n

\u00a0The\u00a0<\/span><\/b>efficiency (\u03b7) of a receiver is defined\u00a0<\/span><\/b>as\u00a0<\/span><\/b>the\u00a0<\/span><\/b>ratio between its useful power (P\u00a0<\/span><\/b>u<\/span><\/b><\/sub>\u00a0) and its total power P\u00a0<\/span><\/b>t<\/span><\/b><\/sub>\u00a0):<\/span><\/b><\/p>\n

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 <\/p>\n

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

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<\/a><\/a>\"\"<\/p>\n

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If you\u00a0<\/span><\/b>stop the shaft of an electric motor,\u00a0<\/span><\/b>it will act as a\u00a0<\/span><\/b>resistor, with all its electrical energy being transformed into thermal energy, which could burn it out.<\/span><\/b><\/p>\n

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The\u00a0<\/span><\/b>electrical power that the generator delivers to the receiver is the generator’s useful power\u00a0<\/span><\/b>(Ui).<\/b><\/span><\/b><\/b><\/b><\/p>\n

For the\u00a0<\/span><\/b>receiver, this same power represents the total power.\u00a0<\/span><\/b>Of this total, a\u00a0<\/span><\/b>portion is useful (E’.i) and the other is dissipated (r’.i\u00a0<\/span><\/b>2<\/span><\/b><\/sup>\u00a0).\u00a0<\/span><\/b>Observe the diagram below carefully.<\/span><\/b><\/p>\n

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Pouillet’s Law\u00a0<\/span><\/b>\u2013\u00a0<\/span><\/b>Single-loop electrical circuit with generators and receivers<\/span><\/b><\/p>\n

Let there be a\u00a0<\/span><\/b>generator of electromotive force (emf) and internal resistance r, a receiver of counter-electromotive force (fcem) E’ and internal resistance r’ and a resistor of resistance R, associated in series\u00a0<\/span><\/b>as shown in the figure,\u00a0<\/b>constituting a\u00a0<\/b>single-mesh electrical circuit.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/p>\n

As they are in\u00a0<\/span><\/b>series, the intensity of the electric current i is the same in each device.<\/span><\/b><\/p>\n

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The\u00a0<\/span><\/b>generator creates at its terminals A and B a ddp (voltage) U\u00a0<\/span><\/b>that causes a potential\u00a0<\/span><\/b>rise\u00a0<\/span><\/b>and that must be equal to the sum of the potential drops caused by the resistor U’ and the\u00a0<\/b>receiver U”, that is, U = U’ + U”\u00a0<\/b>U = E \u2013 ri\u00a0\u00a0<\/b>\u00a0 U’ = Ri\u00a0\u00a0<\/b>\u00a0 U’ = E’ + r’.i\u00a0<\/b>\u00a0 E \u2013 ri = Ri + E’ + r’.i\u00a0\u00a0<\/b>\u00a0 E \u2013 E’=(r + r’ + R).i\u00a0\u00a0<\/b>\u00a0 i=(E \u2013 E’)\/(r + r’ + R)\u00a0\u00a0<\/b>\u00a0 generalizing\u00a0\u00a0<\/b>\u00a0 in single-mesh circuits:<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b>\"\"\"\"<\/b>\u00a0\u00a0\"\"\"\"\"\"\"\"\"\"<\/b><\/p>\n

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Analyze\u00a0<\/span><\/b>this example carefully:\u00a0<\/span><\/b>In\u00a0<\/span><\/b>the circuit diagram below, determine:<\/span><\/b><\/p>\n

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a)\u00a0<\/span><\/b>the\u00a0<\/span><\/b>intensity of the electric current in the generator, in the receiver and in the 5\u03a9 resistance.<\/span><\/b><\/p>\n

b)\u00a0<\/span><\/b>The\u00a0<\/span><\/b>potential difference at the terminals of the generator, the receiver and the 5\u03a9 resistor.<\/span><\/b><\/p>\n

 <\/p>\n

a)\u00a0<\/span><\/b>As the\u00a0<\/span><\/b>direction of the electric current is not specified,\u00a0<\/span><\/b>it\u00a0<\/span><\/b>follows the direction of the highest emf, which is that of the\u00a0<\/span><\/b>generator,\u00a0<\/b>where the\u00a0<\/b>current leaves through the positive pole.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/p>\n

In this case, the\u00a0<\/span><\/b>17V emf is the generator\u00a0<\/span><\/b>and the\u00a0<\/span><\/b>current in the circuit is in the counterclockwise direction,\u00a0<\/span><\/b>since the\u00a0<\/span><\/b>current\u00a0<\/span><\/b>comes out of the positive pole of the circuit. The circuit\u00a0<\/b>must be\u00a0<\/b>transformed into a single-mesh circuit and, thus, the parallel association must be resolved (8\/2 = 4\u03a9).<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Applying\u00a0<\/span><\/b>Pouillet’s law\u00a0<\/span><\/b>i = (\u2211E \u2013 \u2211E’)\/\u2211R\u00a0<\/b>= (17 \u2013 10)\/(4 + 2 + 1 + 5 + 2)\u00a0\u00a0<\/b>\u00a0 i = 7\/14\u00a0\u00a0<\/b>i =\u00a0<\/b>0.5A\u00a0<\/b>, which is the\u00a0<\/b>same through all elements of the circuit, as they are in series.<\/b><\/span>\u00a0\"\"\u00a0\u00a0\u00a0<\/b><\/b>\"\"\"\"\u00a0<\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

b)\u00a0<\/span><\/b>Generator\u00a0<\/b>U\u00a0<\/b>g<\/b><\/sub>\u00a0= E \u2013 ri\u00a0<\/b>= 17 \u2013 2.0.5\u00a0\u00a0<\/b>U\u00a0<\/b>g<\/b><\/sub>\u00a0= 16V\u00a0<\/b>receiver\u00a0<\/b>U\u00a0<\/b>r<\/b><\/sub>\u00a0= E’ + r’.i\u00a0<\/b>= 10 + 1.0.5\u00a0\u00a0<\/b>U\u00a0<\/b>r<\/b><\/sub>\u00a0= 9.5V\u00a0<\/b>U\u00a0<\/b>5\u03a9<\/b><\/sub>\u00a0= Ri\u00a0<\/b>= 5.0.5\u00a0\u00a0<\/b>U\u00a0<\/b>5\u03a9<\/b><\/sub>\u00a0= 2.5V.<\/b><\/span>\u00a0<\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\u00a0<\/b>\u00a0\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0<\/b>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/p>\n

 <\/p>\n

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

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

POUILLET’S LAW \u2013 RECEPTORS Receivers \u2013 Association of generators with receivers \u2013 Pouillet\u2019s Law Electrical receiver A\u00a0device\u00a0that\u00a0converts electrical energy into another form of energy, not exclusively thermal. Examples:\u00a0electric motors, fans, blenders, refrigerators, stereos, videos, cell phones, computers, etc. A\u00a0fan, for example\u00a0,\u00a0converts thermal energy into mechanical energy;\u00a0this\u00a0conversion,\u00a0however,\u00a0is not complete,\u00a0as\u00a0part of the energy is inevitably converted into thermal energy. Characteristic quantities of<\/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-11312","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11312","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=11312"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11312\/revisions"}],"predecessor-version":[{"id":12011,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11312\/revisions\/12011"}],"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=11312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}