Experiment 6-The RC Constant Time - The RC Time Constant...

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The RC Time Constant Christian Lawrence Neha Manikonda Pritesh Patel Yasmine Hill 2/25/10 Instructor: Sonal Singh
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Abstract In this experiment how a capacitor charges and discharges in a RC circuit was observed. In addition, the RC time constant (τ = RC) was observed. To study the charging/discharging of the capacitor, the voltage increases/decreases with time across the capacitor were considered. The following formulas were used: V=V o (1-e -t/RC )=V o (1-e -t/τ ) (charging voltage) and V=V o e -t/RC (discharging voltage). Once the charging and discharging voltages were recorded in the data table, the slope of the voltages was found by taking the natural logarithm of the previous equations: ln (V o -V) = + ln V o (charging voltage) and ln V = + ln V o (discharging voltage). The RC constant for each data table was 51 and 100 respectively; the percent error for each table was 0.47 % and 2.44 % respectively. The RC constant and the percent error illustrate the validity of this method of determining the RC time constant. Introduction Capacitors are able to store and release charges when they are connected and disconnected from a voltage source. When a capacitor is charging, its charge increases until it reaches the maximum voltage of the source. By combining both Ohm’s Law and Kirchoff’s Current Law, the following equation is can be derived: where V o is the initial voltage, I is the current, R is the resistance, Q the charge and C the capacitance. From this equation, the following two equations were derived to calculate the charging capacitor and discharging capacitor. The charging capacitor equation is: and the
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discharging capacitor equation is: . The previously stated equations can find a voltage at any given time based on the initial voltage and quantity RC that is the resistance
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Experiment 6-The RC Constant Time - The RC Time Constant...

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