The RC Circuit and Time Constant Lab Report, Lab Reports of Physics

Download The RC Circuit and Time Constant Lab Report and more Lab Reports Physics in PDF only on Docsity!                 The ​ ​RC ​ ​Circuit ​ ​& ​ ​Time ​ ​Constant  Lab​ ​Report​ ​007                    ​ ​Professor ​ ​Todd ​ ​R.​ ​Gelbord  Report ​ ​Written​ ​By​ ​Galib​ ​F. ​ ​Rahman  PHYS​ ​1442​ ​Section​ ​D783  November​ ​10,​ ​2017        Table ​ ​of ​ ​Contents    Objective 3  Theory 3  Charging​ ​a​ ​Capacitor 3  Discharging​ ​a​ ​Capacitor 4  Materials 4  Procedure 5  Data 7  DataStudio​ ​Graphs 7  Logarithmic​ ​Graphs 8  Table 10  Computations​ ​&​ ​Source​ ​of​ ​Error 11  Questions 11  Conclusion 11  Procedure  First​ ​we​ ​constructed​ ​the​ ​circuit​ ​as​ ​shown​ ​below: We​ ​set​ ​the​ ​power​ ​supply​ ​voltage​ ​to​ ​3.9​ ​Volts​ ​and​ ​the​ ​resistance​ ​,​R​,​ ​to​ ​1000​ ​Ω.​ ​The​ ​voltage sensors​ ​are​ ​connected​ ​to​ ​​ ​the​ ​PASCO​ ​CI-750​ ​Science​ ​Workshop​®​​ ​750​ ​Interface,​ ​such​ ​that​ ​the​ ​voltage across​ ​the​ ​resistor​ ​is​ ​connected​ ​to​ ​the​ ​analog​ ​input​ ​​Channel​ ​A​​ ​and​ ​the​ ​voltage​ ​across​ ​the​ ​capacitor is​ ​connected​ ​to​ ​the​ ​analog​ ​input​ ​​Channel​ ​B​ ​​(as​ ​highlighted​ ​in​ ​the​ ​picture​ ​below). After​ ​the​ ​circuit​ ​we​ ​built,​ ​was approved,​ ​we​ ​proceeded​ ​to​ ​connect​ ​the sensors​ ​to​ ​DataStudio​ ​and​ ​initialized tables​ ​for​ ​both​ ​channels​ ​alongside their​ ​corresponding​ ​graphs. Next,​ ​we​ ​began​ ​the​ ​charging​ ​process of​ ​the​ ​capacitor,​ ​by​ ​moving​ ​the​ ​SPDT switch​ ​to​ ​position​ ​​1​​ ​(as​ ​shown​ ​in​ ​the schematic​ ​below),​ ​while simultaneously​ ​initiating​ ​the​ ​collection of​ ​data​ ​from​ ​the​ ​sensors​ ​in​ ​DataStudio. We​ ​terminated​ ​the​ ​data collection​ ​once​ ​the​ ​voltage​ ​of​ ​the capacitor​ ​reached​ ​the​ ​same​ ​magnitude of​ ​the​ ​output​ ​voltage,​ ​​ε​. ​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​Charging​ ​Phase To​ ​begin​ ​the​ ​discharging​ ​phase​ ​of​ ​the​ ​capacitor,​ ​we​ ​moved​ ​the​ ​switch​ ​to​ ​position​ ​​2​(as shown​ ​in​ ​the​ ​schematic​ ​below),​ ​while​ ​simultaneously​ ​initiating​ ​the​ ​data​ ​collection​ ​from​ ​the​ ​sensors in​ ​DataStudio. ​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​Discharging​ ​Phase We​ ​terminated​ ​the​ ​data​ ​collection​ ​once​ ​the​ ​voltage​ ​of​ ​the​ ​capacitor​ ​decreased​ ​to​ ​zero.         Data  DataStudio ​ ​Graphs  Run​ ​001:​ ​Charging​ ​phase​ ​of​ ​Capacitor Run​ ​002:​ ​Discharging​ ​Phase​ ​of​ ​Capacitor Channel​ ​A:​ ​Resistor Channel​ ​B:​ ​Capacitor   Table  Input​ ​Voltage ε​=​ ​3.9​ ​V Resistance R​=1000​ ​Ω Capacitance C​=​ ​3.82​ ​mF Slope​ ​from​ ​the​ ​graph​ ​for​ ​the​ ​charging​ ​process Slope​=​ ​​-0.2233​ ​​s​-1 Time​ ​constant​ ​for​ ​the​ ​charging​ ​process​ ​𝛕=​ ​-1/​Slope 4.48​ ​s Slope​ ​from​ ​the​ ​graph​ ​for​ ​the​ ​discharging​ ​process Slope​=​-0.2233​ ​​s​-1 Time​ ​constant​ ​for​ ​the​ ​discharging​ ​process​ ​𝛕=​ ​-1/​Slope4.48​ ​s The​ ​average​ ​value​ ​for​ ​the​ ​time​ ​constant 𝛕=​4.48​ ​s %​ ​difference=​ ​​0% Time​ ​constant​ ​𝛕=​RC 𝛕=​3.82​ ​s %​ ​difference=​ ​​15.9​ ​%               Computations​ ​&​ ​Source​ ​of​ ​Error  [All​ ​graphical​ ​computations​ ​were​ ​performed​ ​on​ ​Excel] Sample ​ ​Percent ​ ​Difference ​ ​Computation  One​ ​possible​ ​source​ ​of​ ​error,​ ​is​ ​the​ ​resistance​ ​of​ ​the​ ​wires​ ​utilized​ ​in​ ​the​ ​construction​ ​of​ ​this circuit.​ ​In​ ​our​ ​calculations​ ​of​ ​​RC​​ ​the​ ​only​ ​resistance​ ​accounted​ ​for​ ​was​ ​the​ ​resistance​ ​of​ ​the​ ​​resistor box​.​ ​Thus,​ ​additional,​ ​potential​ ​resistance​ ​may​ ​affect​ ​the​ ​accuracy​ ​of​ ​the​ ​data​ ​collected. Questions  1. Show​ ​that​ ​the​ ​product​ ​​RC​ ​ ​has​ ​a​ ​dimension​ ​of​ ​second​ ​when​ ​​R​​ ​is​ ​in​ ​Ohms​ ​and​ ​​C​​ ​is​ ​in​ ​Farads. 2. Figure​ ​10.5​ ​shows​ ​plots​ ​of​ ​​V​R​(​t​)​ ​(dotted​ ​line​ ​&​ ​solid​ ​line)​ ​for​ ​two capacitors​ ​that​ ​separately​ ​discharge​ ​through​ ​the​ ​same​ ​resistor. Rank​ ​the​ ​plot​ ​according​ ​to​ ​the​ ​capacitance​ ​of​ ​the​ ​capacitors,​ ​with the​ ​greater​ ​one​ ​first. The​ ​greater​ ​the​ ​time​ ​constant​ ​is,​ ​in​ ​magnitude,​ ​the​ ​longer it​ ​takes​ ​for​ ​the​ ​capacitor​ ​to​ ​charge​ ​and​ ​discharge.​ ​Since​ ​the​ ​time​ ​constant, 𝛕,​ ​is​ ​equal​ ​to​ ​the​ ​product​ ​of​ ​the​ ​resistance,​ ​​R​ ​​,​ ​and​ ​capacitance,​ ​​C​ ​​,​ ​the​ ​“un-dotted”​ ​​ ​curve​ ​represents the​ ​discharging​ ​curve​ ​of​ ​the​ ​capacitor​ ​that​ ​has​ ​greater​ ​capacitance,​ ​in​ ​this​ ​case.​ ​On​ ​the​ ​other​ ​hand the​ ​dotted​ ​curve,​ ​which​ ​approaches​ ​zero​ ​at​ ​a​ ​faster​ ​rate,​ ​is​ ​representative​ ​of​ ​the​ ​discharging capacitor​ ​with​ ​the​ ​lesser​ ​capacitance. Conclusion  In​ ​this​ ​experiment,​ ​we​ ​constructed​ ​a​ ​RC​ ​circuit​ ​and​ ​observed​ ​the​ ​charging​ ​and​ ​discharging​ ​phases of​ ​a​ ​capacitor.​ ​In​ ​addition,​ ​we​ ​deduced​ ​the​ ​time​ ​constant​ ​from​ ​the​ ​slope​ ​of​ ​​ ​natural​ ​log​ ​functions,​ ​for both​ ​the​ ​charging​ ​and​ ​discharging​ ​processes.​ ​After​ ​deducing​ ​the​ ​time​ ​constant​ ​from​ ​graphical analysis,​ ​we​ ​compared​ ​it​ ​to​ ​the​ ​product​ ​of​ ​the​ ​resistance​ ​of​ ​the​ ​resistor​ ​in​ ​the​ ​circuit​ ​and​ ​the capacitance​ ​of​ ​the​ ​capacitor,​ ​to​ ​verify​ ​the​ ​accuracy​ ​of​ ​the​ ​methods​ ​in​ ​deducing​ ​𝛕.