Capacitance and the Oscilloscope

# Capacitance and the Oscilloscope - Michael Lin Partners...

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Michael Lin Tuesday Section Partners: Josh Narciso, Bryant Rolfe Due Date: 04/17/07 Capacitance and the Oscilloscope Michael Lin The objective of this experiment was study the workings of a capacitor as it charged and discharged at DC, to observe the behavior of combinations of multiple capacitors within a circuit, and to learn to use an oscilloscope. Separate circuits were set up to measure the charging and discharging of a capacitor via an ammeter, and then the currents measured by the ammeter were recorded. Charge/discharge cycles were observed in the oscilloscope through a function generator, and the time constants were recorded for different frequencies set on the generator. The time constants obtained from charging and discharging circuits with different size capacitors produced results that were within 3σ in value. The measurement of the time constant with an oscilloscope was 840μs, which was a 1.93% error. INTRODUCTION A capacitor is a device used to store electrical charge and energy. The simplest model of a capacitor is a set of parallel plates; when a charge difference is placed between the two plates, a potential difference forms between them. The amount of charge that a capacitor can store is directly proportional to the voltage given to charge the capacitor, and the proportionality constant is also known as the capacitance. Q = CV ; where C = capacitance, V = voltage, and Q = amount of charge The configuration of the plates (distance between the plates, how the plates are aligned, etc.) are factors that affect how much charge the plates can store. The dependence between the potential storage charge and the configuration is reflected in the constant C. For any given plate geometry, the capacitance takes on the general form of: C = (Geometry factor units of length) * ε 0 A capacitor can be charged by using a battery to establish a voltage across the device; however, the capacitor plates will not immediately gain the full charge of Q = CV, where V is the voltage from the battery. Instead, the capacitor will gradually fill with charge, where the rate of charging decreases smoothly with time. In the charging of a capacitor, there is a quantity RC, also known as the time constant of the circuit, that sets up the time scale for how long it takes to fill the capacitor up to a certain level – the larger the capacitor the longer it takes for the battery to charge it to its maximum charge. A capacitor already filled with charge Q = CV can be discharged if a wire is used to “short” the two plates, which allows the charge to flow freely between them. The discharge of a capacitor is also not instantaneous, and will also occur at a rate that depends on the size of the capacitor and the internal resistance of the wire. When comparing the discharging of a capacitor with the charging, the current that flows when discharging is just like the current in a charging capacitor. The difference between charging and discharging of the capacitor is that the two currents flow in opposite directions; however, the two only differ by sign, and not by absolute value.

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