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,