Charging and Discharging Capacitors in RC Circuits Circuits Trisha Trisha Gatdula, Edson David, Jherome Co, Roma Cruz, Jan Arthur Consolacion Institute of Mathematical Mathematical Sciences Sciences and Physics, Physics, University of the Philippines Philippines Los Banos Banos
Introduction When an uncharged capacitor and resistor are connected in series to a voltage source, charge will flow until the capacitor becomes fully charged, in which the charge stored on its plates is given by Q=CV, Q=CV, where C is the capacitance of the capacitor and V is the voltage. Once the voltage source is removed, the charge on the capacitor returns to zero and the capacitor discharges. discharges. n this paper, the non!steady electric field with resistor and capacitor will be discussed as well as the relation of time with the potential drop and current across the resistor and capacitor. "his paper see#s to e$plain the ability of a capacitor to store charge and provide a potential difference when completely charged and discharged and to determine e$perimentally from the graph the time constant of the %C circuit.
Methodology "wo "wo set ups were made in determining the time constant and voltage drop across the resistor for both charging and and discharging discharging capacitor in an %C circuit driven by a dc voltage. voltage. "he power capacitance capacitance in a &'u( capacitor and resistance in ) *ega ohms resistor were measured initially. (or charging, charging, the resistor and capacitor were connected in series in breadboard, ma#ing sure that the capacitor is fully discharge before closing the the circuit. "hen, "hen, the %C combination was was connected to a battery and, the varying voltage drop across and current through the resistor were recorded for interval of every ) seconds. "his is done for & trials. "he connection was removed at e$actly &+' seconds. fter fter gathering the data, the values were plotted. (or discharging capacitor, capacitor, the end of the resistor to the other end of the capacitor was connected -the device used for charging capacitor). "he circuit is not connected to a battery for this time. "he voltage drop and the current were also recorded twice. "hen the values collected upon reaching &+' seconds were plotted. plotted.
Results and Discussion
(igure )!./otential drop across the resistor and capacitor during charging
(igure )!&. Current through the resistor and accumulated charges on the plate of the capacitor during charging
(igure )!0. /otential drop across the resistor and capacitor during discharging
(igure )!+. Current through the resistor and accumulated charges on the plate of the capacitor during discharging
n this e$periment, we see how the charging and discharging process ta#es place in a basic %C circuit. 1uring the charging process, the potential drop across the resistor started at .232)V and ended up at around '.&04V. 5imultaneously the current was measured at the same time, having an output of '.0 at t=', and ' at t=&+'s. 1uring the set up, the team used two resistors in series connection which has a total resistance of ).) *ega Ohms, since there is no single resistor in the lab e6uipment to attain ) mega ohms resistance. n the first attempt to do the e$periment, the group had complications because of a lot of factors li#e, the connection of the resistors and the capacitors to the breadboard, resulting to zero values on each multimeter that is measuring the resistance and the current in the circuit respectively. t the time we fi$ed the circuit and made sure all wires and each resistor and capacitor were connected properly then the e$periment goes on. 7very five seconds, starting at zero second, we measure each value of the voltage through the resistors and also the current through the capacitor. t can be seen in the graph that both have values that are decreasing. "hese results support the theoretical approach that as one capacitor charges voltage through the resistor, in between the capacitor and the source charge, decreases as the charge is being stored in the capacitor from the battery, though in time, we can see that the current across the resistor and the voltage drop according to the reading in each multimeter, does not reach zero at the same time. "his can be e$plained by the limitation of the device to measure very small amount of current that passes through the given circuit, thus giving a reading of '.'' through what we cannot see are the numbers located way further the decimal point. Whilst in the discharging process, it can be seen in the graph that both the voltage and the current across the resistor suddenly increases in some amount of time though following the graph it also decreases at the time when it has reached its pea#. "his is because the source of the flow of charge now is the charged capacitor already. nd as we release the voltage source, the charge that is instored in the capacitor suddenly in a short amount of time was released thus the charges flow freely throughout the circuit. "he decrease that can be seen in the data however, can be e$plained because at some point all of the stored charges in the capacitor will be released thus the reading in will approach the value of zero in time.
Conclusion n this e$periment, we studied the process of charging and discharging of a capacitor in a %C circuit and the relationship of the potential drop and current to time. n charging the capacitor, the potential drop decreased as the time increased. lso, the current decreased with time. n the discharging process, the potential drop increased for a small amount of time but then decreased with time. "he current also followed the same trend with the potential drop.
Reerences . 8. 9oung, %. (reedman, :;niversity /hysics with *odern /hysics & th 7dition<, Chapter &2.+, /earson 7ducation nc., 5an (rancisco C, &''3. &. :/895 3& aboratory *anual<, 7$ercise ) %C Circuit, /hysics 1ivision *5/, ;/>, &'+.
