PASCO EM-8656 AC_DC ELECTRONICS LABORATORY - Manual (Page 41)

37
012-05892A AC/DC Electronics Laboratory
®
Experiment 12: RC Circuit
EQUIPMENT NEEDED:
– Computer and Science Workshop™ Interface
– Power Amplifier (CI-6552A)
– Voltage Sensor (CI-6503)
– AC/DC Electronics Lab Board (EM-8656): 100
Ω
resistor and 330
µ
F capacitor
– (2) banana plug patch cords (such as SE-9750)
– LRC meter (optional)
Purpose
The purpose of this experiment is to investigate how the voltage across a capacitor varies as it
charges and to find the capacitive time constant.
Theory
When an uncharged capacitor is connected across a DC voltage source, the rate at which it
charges up decreases as time passes. At first, the capacitor is easy to charge because there is very
little charge on the plates. But as charge accumulates on the plates, the voltage source must “do
more work” to move additional charges onto the plates because the plates already have charge of
the same sign on them. As a result, the capacitor charges exponentially, quickly at the beginning
and more slowly as the capacitor becomes fully charged. The charge on the plates at any time is
given by:
q = q
o
1
−
e
− t
τ
( )
where q
o
is the maximum charge on the plates and
τ
is the capacitive time constant (
τ
= RC,
where R is resistance and C is capacitance).
➤ NOTE: The stated value of a capacitor may vary by as much as ±20% from the actual value.
Taking the extreme limits, notice that when t = 0, q = 0 which means there is not any charge
on the plates initially. Also notice that when t goes to infinity, q goes to q
o
which means it
takes an infinite amount of time to completely charge the capacitor.
The time it takes to charge the capacitor to half full is called the half-life and is related to the time
constant in the following way:
t
1
2
= τ
ln2
In this experiment the charge on the capacitor will be measured indirectly by measuring the
voltage across the capacitor since these two values are proportional to each other: q = CV.