{"id":2935,"date":"2020-08-03T13:40:29","date_gmt":"2020-08-03T17:40:29","guid":{"rendered":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/?page_id=2935"},"modified":"2021-08-30T17:05:26","modified_gmt":"2021-08-30T21:05:26","slug":"f21","status":"publish","type":"page","link":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/f21\/","title":{"rendered":"Lab 1 Background F21"},"content":{"rendered":"<p>During the next two weeks in lab, we will investigate some basic concepts of electrical circuits. The study of electronics is largely a study of the behavior and relationship of two quantities &#8211; <em>voltage<\/em> and <em>current<\/em>. Current \\(I\\) is defined as the rate of electrical charge moving <strong>through<\/strong> a circuit. Its SI unit is the ampere \\(\\rm{A}\\).\u00a0 One amp is equal to one coulomb \\(\\rm{C}\\) of charge per second: \\(1\\:\\rm{A} = 1\\:\\rm{C\/s}\\). Voltage is defined as the amount of energy required to move a unit of charge from one location in a circuit to another location in the circuit. Thus there is an energy per unit of charge drop between or <strong>across<\/strong> the two locations.\u00a0 The unit of voltage is the Volt.\u00a0 One volt is equal to one joule \\(\\rm{J}\\) per coulomb: \\(1\\:\\rm{V} = 1\\:\\rm{J\/C}\\).<\/p>\n<p>A fundamentally related quantity is <em>resistance<\/em>, defined for any device or circuit element as the ratio of the voltage across that device to the current flowing through it, $$R=\\frac{V}{I}.$$<\/p>\n<p id=\"ohmic\">Think of resistance as a measure of how hard it is to get current to flow in a device or circuit element. High resistance circuits can have high current only if high voltages are applied, while low resistance circuits can carry high current even at low voltages. A conductor like a <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/#AlligatorClipLeads\">small piece of copper wire<\/a> has negligible resistance (less than \\(1 \\Omega\\)), whereas <a href=\"http:\/\/hemingray.info\/database\/index.php\">good insulators like glass<\/a> have several million ohms of resistance or more.\u00a0 The resistance \\(R\\) has units of volts per amp, defined to be an ohm \\(\\Omega\\): \\(1\\:\\Omega = 1\\:\\rm{V\/A}\\). Note: the resistance of a device may depend on the amount of current flowing through it. If \\(R\\) does not depend on the current, the device is said to be &#8220;ohmic&#8221;.<\/p>\n<p>In the laboratory we have a number of standard <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/#CarbonResistors\">carbon resistors<\/a> (ohmic devices), color coded as follows:<\/p>\n<ul>\n<li>\\(0\\)-black<\/li>\n<li>\\(1\\)-brown<\/li>\n<li>\\(2\\)-red<\/li>\n<li>\\(3\\)-orange<\/li>\n<li>\\(4\\)-yellow<\/li>\n<li>\\(5\\)-green<\/li>\n<li>\\(6\\)-blue<\/li>\n<li>\\(7\\)-violet<\/li>\n<li>\\(8\\)-gray<\/li>\n<li>\\(9\\)-white<\/li>\n<\/ul>\n<p>The first two colors signify the first two significant figures of the resistance value and the third gives the number of zeros to add to them. For example, brown-black-orange would be \\([1-0-000]\\) or \\(10,000\\:\\Omega\\). The fourth color is the uncertainty: gold for \\(\\pm 5\\%\\), silver for \\(\\pm 10\\%\\).<\/p>\n<h2>Connections in series versus in parallel:<\/h2>\n<ul class=\"indentedh2\">\n<li>Resistors in Series: The applied voltage, \\(V\\), drives a current though these resistors in <em>series<\/em>. Each resistor has the <em>same current<\/em>, \\(I\\), through it.\n<p><div id=\"attachment_1182\" style=\"width: 227px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1182\" class=\"wp-image-1182 size-full\" src=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinSeries.png\" alt=\"ResistorsinSeries\" width=\"217\" height=\"192\" srcset=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinSeries.png 217w, https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinSeries-150x133.png 150w\" sizes=\"auto, (max-width: 217px) 100vw, 217px\" \/><p id=\"caption-attachment-1182\" class=\"wp-caption-text\">Resistors in series<\/p><\/div><\/li>\n<li>Resistors in Parallel: The applied voltage, \\(V\\), drives a current through these resistors in <em>parallel<\/em>. Each resistor has the <em>same voltage drop<\/em>, \\(V\\), across it.\n<p><div id=\"attachment_1181\" style=\"width: 197px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1181\" class=\"wp-image-1181 size-full\" src=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinParallel.png\" alt=\"ResistorsinParallel\" width=\"187\" height=\"210\" srcset=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinParallel.png 187w, https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/ResistorsinParallel-134x150.png 134w\" sizes=\"auto, (max-width: 187px) 100vw, 187px\" \/><p id=\"caption-attachment-1181\" class=\"wp-caption-text\">Resistors in parallel<\/p><\/div><\/li>\n<\/ul>\n<h2>Measuring Current and Voltage<\/h2>\n<ul class=\"indentedh2\">\n<li>Current: To measure current, the <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/#DigitalMultimeters\">ammeter<\/a> (current meter) must be part of the circuit so that all the current to be measured flows <strong>through<\/strong> it &#8211; the ammeter must be <em>in series<\/em> with the components carrying the current to be measured. Ideally, the ammeter should not affect the current of the circuit it is part of, and therefore should have close to zero resistance.\n<p><div id=\"attachment_1179\" style=\"width: 286px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1179\" class=\"wp-image-1179 size-full\" src=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureCurrent.png\" alt=\"MeasureCurrent\" width=\"276\" height=\"150\" srcset=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureCurrent.png 276w, https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureCurrent-150x82.png 150w\" sizes=\"auto, (max-width: 276px) 100vw, 276px\" \/><p id=\"caption-attachment-1179\" class=\"wp-caption-text\">Measure current in series<\/p><\/div><\/li>\n<li>Voltage: To measure voltage drop between two locations of a circuit, the <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/#DigitalMultimeters\">voltmeter<\/a> must be connected <em>in parallel<\/em> to the part of the circuit <strong>across<\/strong> which we want to measure the voltage drop. Ideally, the voltmeter should draw as little current as possible away from the circuit, and so should have very high resistance.\n<p><div id=\"attachment_1180\" style=\"width: 321px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1180\" class=\"wp-image-1180 size-full\" src=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureVoltage.png\" alt=\"MeasureVoltage\" width=\"311\" height=\"139\" srcset=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureVoltage.png 311w, https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureVoltage-150x67.png 150w, https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/MeasureVoltage-300x134.png 300w\" sizes=\"auto, (max-width: 311px) 100vw, 311px\" \/><p id=\"caption-attachment-1180\" class=\"wp-caption-text\">Measure voltage in parallel<\/p><\/div><\/li>\n<\/ul>\n<h2>Overview of the Electrical Circuits Labs<\/h2>\n<p class=\"indentedh2\">This is a two-week unit. In Lab 1 we will look at what it means for a device (in this case, a <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/#TinyLightbulbwithAttachedLeads\">light bulb<\/a>) to be connected in series or parallel with another device. We will then verify <em>Ohm&#8217;s Law<\/em>, \\(V\\propto I\\) for an ohmic device &#8211; specifically a carbon resistor &#8211; in which the resistance does not vary with the amount of current flowing through it. In <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/lab-2-electrical-circuits-capacitance\/\">Lab 2<\/a> we will investigate capacitance.<\/p>\n<p class=\"indentedh2\"><a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-2\/\">Equipment<\/a> <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-3\/\">Data Collection and Analysis<\/a> <a href=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-2\/physics-1140-lab-1-electrical-circuits-basic-electrical-concepts-and-measurements-3-4\/\">Summary Questions<\/a><\/p>\n<p class=\"centered\"><a href=\"http:\/\/www.mathjax.org\"> <img decoding=\"async\" title=\"Powered by MathJax\" src=\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2015\/08\/badge7.gif\" alt=\"Powered by MathJax\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>During the next two weeks in lab, we will investigate some basic concepts of electrical circuits. The study of electronics is largely a study of the behavior and relationship of two quantities &#8211; voltage and current. Current \\(I\\) is defined as the rate of electrical charge moving through a circuit. Its SI unit is the [&hellip;]<\/p>\n","protected":false},"author":293,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2935","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/pages\/2935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/users\/293"}],"replies":[{"embeddable":true,"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/comments?post=2935"}],"version-history":[{"count":0,"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/pages\/2935\/revisions"}],"wp:attachment":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/media?parent=2935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}