Physics 2402
Department of Physics and Geology
RC Circuits
Purpose
The purpose of this lab is to understand how capacitors charge and discharge.
Materials
Decade Resistance Box (CENCO), 0.1 µF, 0.5µF, and 1.0 µF Capacitors, 2001 Function Generator, GW
INSTEK Oscilloscope (GOS-620), red and black cords, clips, and coaxial heads.
Theory
If a resistor is connected to an AC voltage source that outputs a square-wave signal, then you can
observe a square-wave voltage through an oscilloscope connected in parallel to the resistor (Figure 1).
However, if one includes a capacitor in the circuit and observe the voltage drop on the capacitor, he can
see the square-wave signal modified as shown in Figure 2. The shape of the modified signal depends on
the capacitance because a capacitor takes time to charge and discharge, which is quite different from a
resistor.
Charge gradually
Discharge gradually
Figure 1. Square wave signal on resistor.
Figure 2. Modified wave signal on capacitor.
One can analyze the time needed to charge a capacitor to any fraction of the full voltage (V0), and the
time needed to discharge the capacitor to any fraction of its full voltage (V0). Illustrated in Figure 3 are
some representative fractions, 0.25, 0.50, and 0.75.
Figure 3. Voltage versus time on capacitor.
During the charge process, the voltage increases with time as
V(t) = V0 (1 – e-t/RC)
(1)
And during the discharge process, the voltage decreases with time as
V(t) = V0 e-t/RC
(2)
By measuring the time and the voltage ratio, V(t)/V0, one can easily calculate the product RC which has
the dimension of time and is known as the time constant of the RC circuit. For example, in Figure 3, if
t2= 0.005 seconds (as measured from the start of the rise), then using Eq. (1), we have
V(t) / Vo = 0.5 = 1 – e-0.005/RC ,
(3)
which derives RC=0.0072. Similarly if t4 = 0.002 seconds (as measured from the maximum), then using
Eq. (2), we have
V(t) / Vo = 0.75 = e-0.002/RC ,
(4)
which yields RC=0.0072.
Experimental Procedures
1. Observe a square-wave signal in the oscilloscope: Connect a resistance box (select R=1 KΩ) in series
to the function generator to form a closed circuit. Be sure to use a square-wave signal in the
Function
Generator
function
generator, press 1 K for the RANGE setting, and the coaxial head should connect to the
“TTL” terminal. Connect the oscilloscope to the resistor in parallel to observe a square-wave signal
on the oscilloscope (Refer to Image 1). One can pull out both handles of the oscilloscope and rotate
them in order to set the device at your preferred height. In addition, one can choose either CH1 or
CH2 in the oscilloscope to observe signals as long as you stick with the same one throughout the lab.
0.1 µF capacitor
Adjust frequency in the function generator to observe the changes on the square-wave signal in the
0.1 µF Capacitor
oscilloscope. In terms of the frequency reading of the function generator, for example, if you press
the 1K button, the actual frequency output is 1K multiplied by the fraction shown on the frequency
Resistance BoxOscilloscope
dial. Set frequency dial to 1.0 for this lab.
0.1 µF capacitor
Image 1
Image 2
2
2. Insert the 0.1 µF capacitor in the circuit: Connect the oscilloscope in parallel to the capacitor as
shown in the diagram below and Image 2. Observe the changes on the square-wave signal on
the oscilloscope (Refer to Image 2 and the panel settings in Image 3).
Image 3
Image 4
Resistance is still set at 1 KΩ. If the signal on the oscilloscope keeps moving to the left or the
right, use the “LEVEL” knob to stabilize it. The “POSITION” knobs can move the curve up or
down, left or right.
3. Read the number of divisions which correspond to Voltage and time: “VOLTS/DIV” button refers
to the voltages each division (consisting of five small gradations) on the vertical axis represents.
“TIME/DIV” button indicates the time each division on the horizontal axis represents. For
example, in Image 4 the full voltage is embodied by about 7 vertical divisions, and the time
period is embodied by about 4.8 horizontal divisions. In Image 3, each division on the vertical
and horizontal axes represents .5 volts and .2 ms, respectively. Enter the values in Tables 1(a)
and 1(b). (Refer to Figure 3 and Eqs. (3) and (4) for t1 through t6.)
R= 1000 Ω
C=0.1µF
Table 1 (a). Charging circuit.
V(t)/V0
# of horizontal
divisions
0.25
0.5
0.75
Theoretical value RC = _____________________
TIME/DIV
t (s)
Derived values of
RC
t1 =
t2 =
t3 =
Avg. =
3
Percentage error =
______________________
Table 1(b). Discharging circuit.
V(t)/V0
# of horizontal
divisions
TIME/DIV
0.75
0.5
0.25
t (s)
Derived values of
RC
t4 =
t5 =
t6=
Avg.=
Percentage error=__________________________
4. Repeat Steps 2 and 3, this time using the 0.5 µF capacitor instead of the 0.1 µF capacitor (Refer
to Image 5 below): Use the same oscilloscope settings as in Image 3 and enter values in Tables
2(a) and 2(b).
R= 1000 Ω
C = 0.5 µF
0.5 µF capacitor
5 µF capacitor
0.5 µF capacitor
Theoretical value RC = _________________
Image 5
Table 2 (a). Charging circuit.
V(t)/V0
# of horizontal
divisions
0.25
0.5
0.75
TIME/DIV
t (s)
Derived values of
RC
t1 =
t2 =
t3 =
Avg.=
Percentage error =______________________
4
Table 2 (b). Discharging circuit.
V(t)/V0
# of horizontal
divisions
TIME/DIV
0.75
0.5
0.25
t (s)
Derived values of
RC
t4 =
t5 =
t6=
Avg.=
Percentage error =______________________
5. Repeat Steps 2 and 3, this time using the 1 µF capacitor instead of the 0.1 µF capacitor (Refer to
Image 6 below): Use the same TIME/DIV setting as in Image 3 but change VOLTS/DIV setting to
.1 V and enter values in Tables 3 (a) and 3(b).
R= 1000 Ω
C=1 µF
Theoretical value RC = __________________
1 µF capacitor
Image 6
Table 3 (a). Charging circuit.
V(t)/V0
# of horizontal
divisions
0.25
0.5
0.75
TIME/DIV
t (s)
Derived values of
RC
t1 =
t2 =
t3 =
Avg.=
Percentage error =______________________
5
Table 3 (b). Discharging circuit.
V(t)/V0
# of horizontal
divisions
0.75
0.5
0.25
TIME/DIV
t (s)
Derived values of
RC
t4 =
t5 =
t6=
Avg.=
Percentage error =______________________
Making Connections
How does the capacitance affect the time to charge and discharge a capacitor?
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