{"id":1332,"date":"2017-10-27T16:31:56","date_gmt":"2017-10-27T16:31:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/back-emf\/"},"modified":"2017-11-08T03:26:54","modified_gmt":"2017-11-08T03:26:54","slug":"back-emf","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/back-emf\/","title":{"raw":"Back Emf","rendered":"Back Emf"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Explain what back emf is and how it is induced.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id1169736622182\">It has been noted that motors and generators are very similar. Generators convert mechanical energy into electrical energy, whereas motors convert electrical energy into mechanical energy. Furthermore, motors and generators have the same construction. When the coil of a motor is turned, magnetic flux changes, and an emf (consistent with Faraday\u2019s law of induction) is induced. The motor thus acts as a generator whenever its coil rotates. This will happen whether the shaft is turned by an external input, like a belt drive, or by the action of the motor itself. That is, when a motor is doing work and its shaft is turning, an emf is generated. Lenz\u2019s law tells us the emf opposes any change, so that the input emf that powers the motor will be opposed by the motor\u2019s self-generated emf, called the <span data-type=\"term\" id=\"import-auto-id1169738200549\">back emf<\/span> of the motor. (See <a href=\"#import-auto-id1169737991643\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1169737991643\">\n<div class=\"bc-figcaption figcaption\">The coil of a DC motor is represented as a resistor in this schematic. The back emf is represented as a variable emf that opposes the one driving the motor. Back emf is zero when the motor is not turning, and it increases proportionally to the motor\u2019s angular velocity.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1169737870437\" data-alt=\"Figure shows an electric circuit. The circuit has a cell represented as driving e m f of voltage one hundred and twenty volt is connected in series with a variable e m f source with a range of voltage from zero to one hundred twenty volts and a resistance R. The other end of resistance R is connected to an open switch. The switch is connected back to the Driving e m f cell.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_24_06_01.jpg\" data-media-type=\"image\/jpg\" alt=\"Figure shows an electric circuit. The circuit has a cell represented as driving e m f of voltage one hundred and twenty volt is connected in series with a variable e m f source with a range of voltage from zero to one hundred twenty volts and a resistance R. The other end of resistance R is connected to an open switch. The switch is connected back to the Driving e m f cell.\" width=\"225\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1169738131015\">Back emf is the generator output of a motor, and so it is proportional to the motor\u2019s angular velocity [latex]\\omega [\/latex]. It is zero when the motor is first turned on, meaning that the coil receives the full driving voltage and the motor draws maximum current when it is on but not turning. As the motor turns faster and faster, the back emf grows, always opposing the driving emf, and reduces the voltage across the coil and the amount of current it draws. This effect is noticeable in a number of situations. When a vacuum cleaner, refrigerator, or washing machine is first turned on, lights in the same circuit dim briefly due to the [latex]IR[\/latex] drop produced in feeder lines by the large current drawn by the motor. When a motor first comes on, it draws more current than when it runs at its normal operating speed. When a mechanical load is placed on the motor, like an electric wheelchair going up a hill, the motor slows, the back emf drops, more current flows, and more work can be done. If the motor runs at too low a speed, the larger current can overheat it (via resistive power in the coil, [latex]P={I}^{2}R[\/latex]), perhaps even burning it out. On the other hand, if there is no mechanical load on the motor, it will increase its angular velocity [latex]\\omega [\/latex] until the back emf is nearly equal to the driving emf. Then the motor uses only enough energy to overcome friction.<\/p>\n<p id=\"import-auto-id1169737818275\">Consider, for example, the motor coils represented in <a href=\"#import-auto-id1169737991643\" class=\"autogenerated-content\">(Figure)<\/a>. The coils have a [latex]\\text{0.400}\\phantom{\\rule{0.25em}{0ex}}\\Omega [\/latex] equivalent resistance and are driven by a 48.0 V emf. Shortly after being turned on, they draw a current [latex]I=\\text{V\/R}=\\left(\\text{48}\\text{.}0\\phantom{\\rule{0.25em}{0ex}}\\text{V}\\right)\/\\left(0\\text{.}\\text{400}\\phantom{\\rule{0.25em}{0ex}}\\Omega \\right)=\\text{120}\\phantom{\\rule{0.25em}{0ex}}\\text{A}[\/latex] and, thus, dissipate [latex]P={I}^{2}R=5\\text{.}\\text{76}\\phantom{\\rule{0.25em}{0ex}}\\text{kW}[\/latex] of energy as heat transfer. Under normal operating conditions for this motor, suppose the back emf is 40.0 V. Then at operating speed, the total voltage across the coils is 8.0 V (48.0 V minus the 40.0 V back emf), and the current drawn is [latex]I=\\text{V\/R}=\\left(8\\text{.}0\\phantom{\\rule{0.25em}{0ex}}\\text{V}\\right)\/\\left(0\\text{.}\\text{400}\\phantom{\\rule{0.25em}{0ex}}\\Omega \\right)=\\text{20}\\phantom{\\rule{0.25em}{0ex}}\\text{A}[\/latex]. Under normal load, then, the power dissipated is [latex]P=\\text{IV}=\\left(\\text{20}\\phantom{\\rule{0.25em}{0ex}}\\text{A}\\right)\/\\left(8\\text{.}0\\phantom{\\rule{0.25em}{0ex}}\\text{V}\\right)=\\text{160}\\phantom{\\rule{0.25em}{0ex}}\\text{W}[\/latex]. The latter will not cause a problem for this motor, whereas the former 5.76 kW would burn out the coils if sustained.<\/p>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1169737804196\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1169738150917\">\n<li id=\"import-auto-id1169737879782\">Any rotating coil will have an induced emf\u2014in motors, this is called back emf, since it opposes the emf input to the motor.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1169737946201\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169738051900\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737988090\">\n<p id=\"import-auto-id1169737764505\">Suppose you find that the belt drive connecting a powerful motor to an air conditioning unit is broken and the motor is running freely. Should you be worried that the motor is consuming a great deal of energy for no useful purpose? Explain why or why not.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1169737910281\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737728029\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737818989\">\n<p id=\"import-auto-id1169737735216\">Suppose a motor connected to a 120 V source draws 10.0 A when it first starts. (a) What is its resistance? (b) What current does it draw at its normal operating speed when it develops a 100 V back emf?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169737819685\">\n<p>(a) [latex]12.00 \\Omega [\/latex]<\/p>\n<p id=\"import-auto-id1169738076654\">(b) 1.67 A<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169738010283\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169738110666\">\n<p id=\"import-auto-id1169738084018\">A motor operating on 240 V electricity has a 180 V back emf at operating speed and draws a 12.0 A current. (a) What is its resistance? (b) What current does it draw when it is first started?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737781410\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737918104\">\n<p id=\"import-auto-id1169736863764\">What is the back emf of a 120 V motor that draws 8.00 A at its normal speed and 20.0 A when first starting?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169738088415\">\n<p id=\"import-auto-id1169738079877\">72.0 V<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737946132\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737724474\">\n<p id=\"import-auto-id1169737785555\">The motor in a toy car operates on 6.00 V, developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737854685\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737790350\">\n<p id=\"import-auto-id1169737710254\"><strong data-effect=\"bold\"><strong>Integrated Concepts<\/strong><\/strong><\/p>\n<p id=\"eip-137\">The motor in a toy car is powered by four batteries in series, which produce a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a<br>\n[latex]\\text{0.100 \u03a9}[\/latex]<br>\n internal resistance. What is the resistance of the motor?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169737768658\">\n<p id=\"import-auto-id1169738211405\">[latex]\\text{0.100 \u03a9}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1169736623193\">\n<dt>back emf<\/dt>\n<dd id=\"fs-id1169737785191\">the emf generated by a running motor, because it consists of a coil turning in a magnetic field; it opposes the voltage powering the motor<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Explain what back emf is and how it is induced.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id1169736622182\">It has been noted that motors and generators are very similar. Generators convert mechanical energy into electrical energy, whereas motors convert electrical energy into mechanical energy. Furthermore, motors and generators have the same construction. When the coil of a motor is turned, magnetic flux changes, and an emf (consistent with Faraday\u2019s law of induction) is induced. The motor thus acts as a generator whenever its coil rotates. This will happen whether the shaft is turned by an external input, like a belt drive, or by the action of the motor itself. That is, when a motor is doing work and its shaft is turning, an emf is generated. Lenz\u2019s law tells us the emf opposes any change, so that the input emf that powers the motor will be opposed by the motor\u2019s self-generated emf, called the <span data-type=\"term\" id=\"import-auto-id1169738200549\">back emf<\/span> of the motor. (See <a href=\"#import-auto-id1169737991643\" class=\"autogenerated-content\">(Figure)<\/a>.)<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1169737991643\">\n<div class=\"bc-figcaption figcaption\">The coil of a DC motor is represented as a resistor in this schematic. The back emf is represented as a variable emf that opposes the one driving the motor. Back emf is zero when the motor is not turning, and it increases proportionally to the motor\u2019s angular velocity.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1169737870437\" data-alt=\"Figure shows an electric circuit. The circuit has a cell represented as driving e m f of voltage one hundred and twenty volt is connected in series with a variable e m f source with a range of voltage from zero to one hundred twenty volts and a resistance R. The other end of resistance R is connected to an open switch. The switch is connected back to the Driving e m f cell.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_24_06_01.jpg\" data-media-type=\"image\/jpg\" alt=\"Figure shows an electric circuit. The circuit has a cell represented as driving e m f of voltage one hundred and twenty volt is connected in series with a variable e m f source with a range of voltage from zero to one hundred twenty volts and a resistance R. The other end of resistance R is connected to an open switch. The switch is connected back to the Driving e m f cell.\" width=\"225\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1169738131015\">Back emf is the generator output of a motor, and so it is proportional to the motor\u2019s angular velocity <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8ffb415af81ab9c23c1d2e7ec67d29c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#109;&#101;&#103;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>. It is zero when the motor is first turned on, meaning that the coil receives the full driving voltage and the motor draws maximum current when it is on but not turning. As the motor turns faster and faster, the back emf grows, always opposing the driving emf, and reduces the voltage across the coil and the amount of current it draws. This effect is noticeable in a number of situations. When a vacuum cleaner, refrigerator, or washing machine is first turned on, lights in the same circuit dim briefly due to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e7dc1ee01d4f30de8e50d186dd3b0eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#82;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> drop produced in feeder lines by the large current drawn by the motor. When a motor first comes on, it draws more current than when it runs at its normal operating speed. When a mechanical load is placed on the motor, like an electric wheelchair going up a hill, the motor slows, the back emf drops, more current flows, and more work can be done. If the motor runs at too low a speed, the larger current can overheat it (via resistive power in the coil, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-64cb7d4a802f74c8eecde443ab43485d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#123;&#73;&#125;&#94;&#123;&#50;&#125;&#82;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: 0px;\" \/>), perhaps even burning it out. On the other hand, if there is no mechanical load on the motor, it will increase its angular velocity <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8ffb415af81ab9c23c1d2e7ec67d29c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#109;&#101;&#103;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> until the back emf is nearly equal to the driving emf. Then the motor uses only enough energy to overcome friction.<\/p>\n<p id=\"import-auto-id1169737818275\">Consider, for example, the motor coils represented in <a href=\"#import-auto-id1169737991643\" class=\"autogenerated-content\">(Figure)<\/a>. The coils have a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a44dc0f8d11fbca2ed370066ca52090d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#52;&#48;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#79;&#109;&#101;&#103;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/> equivalent resistance and are driven by a 48.0 V emf. Shortly after being turned on, they draw a current <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-592ce95626058c21f94767c3d20bbe18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#47;&#82;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#56;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#47;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#79;&#109;&#101;&#103;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"309\" style=\"vertical-align: -5px;\" \/> and, thus, dissipate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ec7329d9da82b8769cf7b8aa1ab4b916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#123;&#73;&#125;&#94;&#123;&#50;&#125;&#82;&#61;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#54;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"155\" style=\"vertical-align: 0px;\" \/> of energy as heat transfer. Under normal operating conditions for this motor, suppose the back emf is 40.0 V. Then at operating speed, the total voltage across the coils is 8.0 V (48.0 V minus the 40.0 V back emf), and the current drawn is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-00f844281c4d77661a25730b83034959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#73;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#47;&#82;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#47;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#79;&#109;&#101;&#103;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"291\" style=\"vertical-align: -5px;\" \/>. Under normal load, then, the power dissipated is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c5d33f22bdb8b6fb53224465015c7089_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#86;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#47;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#54;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"272\" style=\"vertical-align: -5px;\" \/>. The latter will not cause a problem for this motor, whereas the former 5.76 kW would burn out the coils if sustained.<\/p>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id1169737804196\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id1169738150917\">\n<li id=\"import-auto-id1169737879782\">Any rotating coil will have an induced emf\u2014in motors, this is called back emf, since it opposes the emf input to the motor.<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1169737946201\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169738051900\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737988090\">\n<p id=\"import-auto-id1169737764505\">Suppose you find that the belt drive connecting a powerful motor to an air conditioning unit is broken and the motor is running freely. Should you be worried that the motor is consuming a great deal of energy for no useful purpose? Explain why or why not.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1169737910281\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737728029\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737818989\">\n<p id=\"import-auto-id1169737735216\">Suppose a motor connected to a 120 V source draws 10.0 A when it first starts. (a) What is its resistance? (b) What current does it draw at its normal operating speed when it develops a 100 V back emf?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169737819685\">\n<p>(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bdc82e87799ce733e5aa6d45f0af028d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#46;&#48;&#48;&#32;&#92;&#79;&#109;&#101;&#103;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id1169738076654\">(b) 1.67 A<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169738010283\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169738110666\">\n<p id=\"import-auto-id1169738084018\">A motor operating on 240 V electricity has a 180 V back emf at operating speed and draws a 12.0 A current. (a) What is its resistance? (b) What current does it draw when it is first started?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737781410\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737918104\">\n<p id=\"import-auto-id1169736863764\">What is the back emf of a 120 V motor that draws 8.00 A at its normal speed and 20.0 A when first starting?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169738088415\">\n<p id=\"import-auto-id1169738079877\">72.0 V<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737946132\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737724474\">\n<p id=\"import-auto-id1169737785555\">The motor in a toy car operates on 6.00 V, developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1169737854685\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1169737790350\">\n<p id=\"import-auto-id1169737710254\"><strong data-effect=\"bold\"><strong>Integrated Concepts<\/strong><\/strong><\/p>\n<p id=\"eip-137\">The motor in a toy car is powered by four batteries in series, which produce a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-02630e5443d2170dabb4989af79e6765_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#49;&#48;&#48;&#32;&Omega;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><br \/>\n internal resistance. What is the resistance of the motor?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1169737768658\">\n<p id=\"import-auto-id1169738211405\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-02630e5443d2170dabb4989af79e6765_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#49;&#48;&#48;&#32;&Omega;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1169736623193\">\n<dt>back emf<\/dt>\n<dd id=\"fs-id1169737785191\">the emf generated by a running motor, because it consists of a coil turning in a magnetic field; it opposes the voltage powering the motor<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1332","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":1290,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1332\/revisions"}],"predecessor-version":[{"id":1333,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1332\/revisions\/1333"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/1290"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1332\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=1332"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1332"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=1332"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=1332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}