LAB# 32
Capacitors
The charge
q
on a capacitor’s plate is proportional to the potential difference
V
across the
capacitor. We express this with
V
q
C
=
,
where
C
is a proportionality constant known as the
capacitance
.
C
is measured in the unit of the
farad, F, (1 farad = 1 coulomb/volt).
If a capacitor of capacitance
C
(in farads), initially charged to a potential
V
0
(volts) is connected
across a resistor
R
(in ohms), a timedependent current will flow according to Ohm’s law. This
situation is shown by the RC (resistorcapacitor) circuit below when the switch is closed.
Figure 1
As the current flows, the charge
q
is depleted, reducing the potential across the capacitor, which
in turn reduces the current. This process creates an exponentially decreasing current, modeled by
.
V t
V e
t
RC
( )
=
!
0
The rate of the decrease is determined by the product
RC
, known as the
time constant
of the
circuit. A large time constant means that the capacitor will discharge slowly.
When the capacitor is charged, the potential across it approaches the final value exponentially,
modeled by
V t
V
e
t
RC
( )
=
!
"
#
$
%
&
’
!
0
1
.
The same time constant
RC
describes the rate of charging as well as the rate of discharging.
OBJECTIVES
•
Measure an experimental time constant of a resistorcapacitor circuit.
•
Compare the time constant to the value predicted from the component values of the
resistance and capacitance.
•
Measure the potential across a capacitor as a function of time as it discharges and as it
charges.
•
Fit an exponential function to the data. One of the fit parameters corresponds to an
experimental time constant.
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APPARATUS
Power Macintosh
100
µ
F nonpolarized capacitor
Universal Lab Interface
10k
Ω
, 400k
Ω
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 Fall '08
 RABE
 Physics, Exponential Function, Capacitance, Charge, Farads, RC time constant

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