1"
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Capacitors
Goal: To study the behavior of capacitors in different types of circuits.
Lab Preparation
A capacitor stores electric charge. A simple configuration for a capacitor is two
parallel metal plates. The amount of charge stored is proportional to the voltage
difference V between the plates. The charge stored on one plate is
Q = CV
where Q is the charge stored, C is the capacitance, and V is the voltage. An equal
amount of opposite charge is induced on the other plate. The capacitance
depends on the area and separation of the plates and any material (called a
dielectric) between the plates.
Figure 1(a) shows typical symbols used to represent capacitors in electrical
schematics. Attaching a capacitor to a battery stores charge on the capacitor
plates as in Figure 1(b). Connecting a resistor to the capacitor as in Figure 1(c)
can drain the stored charge.
Figure 1
When a capacitor is discharged through a resistor R the voltage across the
resistor is VR = IR. The same voltage appears across the capacitor, VC = Q/C.
The capacitor acts like a poor battery that "dies" quickly by giving up all its
stored charge. The charge on the capacitor at a given time is given by
Q = Qo๐!!
!"
where Qo is the charge stored on a capacitor initially. Since VC = Q/C, the voltage
across the capacitor also decays following the same form
V = Vo๐!!
!"
where Vo = Qo/C. A typical exponential decay is shown in Figure 2a.
Figure 2
-
Polar
+++++++
- - - - - -
Vo++++++
- - - - - - I= V(t)
R
Q(t)=CV(t)
R
(a) (b) (c)
V
t
Vo
(a) lnV
t
lnV
o
(b)
B
A
