{"id":62,"date":"2015-07-30T13:32:12","date_gmt":"2015-07-30T13:32:12","guid":{"rendered":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/lab2\/physics-1140-lab-2-electrical-circuits-capacitance\/"},"modified":"2021-08-30T15:02:21","modified_gmt":"2021-08-30T19:02:21","slug":"lab-2-background_f21","status":"publish","type":"page","link":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/lab-2-background_f21\/","title":{"rendered":"Lab 2: Background"},"content":{"rendered":"

Two pieces of equipment that will be very helpful to us in our investigation of capacitance are the function generator<\/a> and the oscilloscope<\/a>.\u00a0 The former produces voltages that are periodic in time \\((\\rm{for\\:example},\\:V(t)=V_{0}\\sin{\\omega t})\\), and the latter allows you to observe and measure these periodic waveforms.\u00a0 In the first part of this lab you will learn how to use these devices by playing with them extensively; no further introduction is needed to begin.\u00a0 However, a brief introduction to capacitors<\/a> and \\(RC\\) circuits is needed for the remainder of the lab.<\/p>\n

A capacitor is a device that stores charge.\u00a0 It turns out that the amount of charge stored (\\(+q\\) on one “plate”, \\(-q\\) on the other) is proportional to the voltage difference \\(\\Delta V\\) across the capacitor, where the proportionality constant \\(C\\) depends on the geometry of the device and on the details of what’s between the plates (vacuum?\u00a0 a cell membrane<\/a>?):$$ q = C \\Delta V.$$<\/p>\n

We call the proportionality constant \\(C\\) the capacitance<\/em>.\u00a0 Don’t confuse it with the abbreviation for coulomb, \\(\\rm{C}\\)!\u00a0 Capacitance is measured in farads, \\(\\rm{F}\\), where \\(1\\:\\rm{F}=1\\:\\rm{C}\/\\rm{V}\\).\u00a0 As you will see, typical capacitors have capacitance values that are only small fractions of a farad.<\/p>\n

It takes time to charge (or discharge) a capacitor.\u00a0 You can show that if you put an uncharged capacitor in series with a battery<\/a> and a resistor<\/a> at \\(t=0\\), the voltage across the capacitor at time \\(t\u22650\\) will be $$\\Delta V = V_{\\rm{batt}}\\left(1-e^{-t\/RC}\\right).$$<\/p>\n

Similarly, if the plates of a charged capacitor are connected by a resistor, the capacitor will discharge according to $$\\Delta V = V_{0}e^{-t\/RC},$$ where \\(V_{0}\\) is the initial voltage across the capacitor.<\/p>\n

We define the time constant \\(\\tau=RC\\), which characterizes how long it takes to charge or discharge a capacitor by some amount; \\(1\\) time constant is the time it takes to gain \\(63\\%\\) of the final charge when charging a capacitor, or to lose \\(63\\%\\) of the initial charge when discharging a capacitor.\u00a0 Measuring time constants for \\(RC\\) circuits provides us with a nice way to measure capacitance if we know resistance, or vice versa.<\/p>\n

Note that this is a two-week lab, with the weeks graded separately.\u00a0 We will stop here in the middle of the Data Collection and Analysis section<\/a> at the end of the first week.<\/p>\n

Equipment<\/a> Data Collection and Analysis<\/a> Summary Questions<\/a><\/p>\n

\"badge\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Two pieces of equipment that will be very helpful to us in our investigation of capacitance are the function generator and the oscilloscope.\u00a0 The former produces voltages that are periodic in time \\((\\rm{for\\:example},\\:V(t)=V_{0}\\sin{\\omega t})\\), and the latter allows you to observe and measure these periodic waveforms.\u00a0 In the first part of this lab you will […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-62","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/pages\/62","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/comments?post=62"}],"version-history":[{"count":0,"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/pages\/62\/revisions"}],"wp:attachment":[{"href":"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-json\/wp\/v2\/media?parent=62"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}