Experiment
27
Date
Course Name
Instructor Name
Student(s) Name
RC Oscilloscope Study
The charge q on a capacitor’s plate is proportional to the potential difference V across the
capacitor. We express this relationship with
q
V  ,
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 V0 (volts) is connected
across a resistor R (in ohms), a time-dependent current will flow according to Ohm’s law. This
situation is shown by the RC (resistor-capacitor) circuit below when the switch is closed.
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 )  V0 e
t
 RC
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
 t
V (t )  V0 1  e RC 


The same time constant RC describes the rate of charging as well as the rate of discharging.
After a time of one time constant t = RC, the voltage is
V = Vo (1 – e(-RC/RC)) = Vo (1 – e(-1)) = 0.63 Vo
That is, the voltage across the capacitor in 0.63 (or 63 %) of its maximum value.
When a square wave ac source is used, the capacitor voltage increases and decreases as the
voltage of the applied signal alternately increases and decreases. Thus, in effect the capacitor
continuously charges and discharges. (NOTE: The high point on the charging curve and the low
point on the decay curve are not V = V0 and V = 0, respectively, since it takes infinite times for
the capacitor to charge and discharge to these values. But if the time constant is several times
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Experiment 27
smaller than half of the period T of the square wave, then to a good approximation, the high and
the low points of the curve may be taken to correspond to V = V0 and V = 0, respectively.)
On an oscilloscope, the time base or the magnitude of the horizontal time axis is determined by
the SWEEP TIME/DIV. From the setting you can determine time functions for traces on the
screen. For example, if there is one complete cycle on the screen and covers 6 horizontal
divisions with a SWEEP TIME/DIV setting at 2 ms/div. Then the time for one cycle is 2 ms/div
x 6 div = 12 ms.
The time constant for an RC circuit is determined by finding the horizontal distance (time)
needed for the trace to reach 0.63 V0.
STUDENT OUTCOMES

Measure an experimental time constant of a resistor-capacitor 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.
MATERIALS
Function Generator (square wave)
Oscilloscope
Connecting wires
Capacitor box
Resistor box
Graphing paper
PRELIMINARY QUESTIONS
1. How is the time base of the horizontal oscilloscope trace determined?
2. Explain how the time constant of the RC circuit is determined from a stationary oscilloscope
pattern.
PROCEDURE
1. Turn on the oscilloscope and the function generator. Set the function generator to 100 HZ and
the wave amplitude to maximum. Connect the square wave output of the function generator
to the vertical input terminal of the oscilloscope.
Check that the small knobs in the center of the VOLTS/DIV and the TIME/DIV controls are
in the Calibrated position. Obtain a stationary trace of one or two cycles on the square wave
pattern on the screen. Adjust the vertical VOLTS/DIV and the function generator smplitude
until the pattern is exactly 8 divisions high. If V0 = 8 divisions, then 5 divisions will
correspond to 0.63 V0 and the corresponding horizontal division will give you the time
constant.
2. Connect the circuit as shown below with C1 = 0.1 F capacitor and R1 = 10 k resistor.
Record the values of your resistor and capacitor in your data table, as well as any tolerance
values marked on them.
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Capacitors
3. Observe the pattern on the screen. Carefully adjust the trigger controls so that the curve starts
upward at the left end of the trace. The exponential rise can be observed in greater detail by
increasing the sweep time (decreasing the TIME/DIV). Adjust the time until the rising curve
extends well across the screen. Be sure that the variable TIME/DIV stays at the calibrated
position.
4. Record in Data Table I.
5. Repeat steps 2 – 4 for R2 = 5 k and R3 = 20 k.
6. Using R1 = 10 k, repeat steps 2 – 3 with C2 = 0.047 F and C3 = 0.2 F.
7. Record in Data Table 2.
DATA TABLE I
Divisions for
0.63 rise
Sweep
time
Exp. time
constant
R
()
C
(F)
RC
(s)
% error
Sweep
time
Exp. time
constant
R
()
C
(F)
RC
(s)
% error
Case 1(R1, C1)
Case 2(R2, C1)
Case 3(R3, C1)
DATA TABLE II
Divisions for
0.63 rise
Case 1(R1, C1)
Case 2(R1, C2)
Case 3(R1, C3)
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Experiment 27
ANALYSIS
1. In the data table, calculate the time constant of the circuit used; that is, the product of
resistance in ohms and capacitance in farads. (Note that 1 F = 1 s).
2. Plot the experimental time constant versus R from Data Table I. Determine the slope of the
straight line that best fits the data points. What does the value of the slope represent?
3. Plot the experimental time constant versus R from Data Table II. Determine the slope of the
straight line that best fits the data points. What does the value of the slope represent?
EXTENSION
Using the knowledge gained in this experiment, determine the experimental value of the given
unknown resistor. Remove the masking tape from the unknown resistor after experimentally
determining its value. Compute the percent error of the measured value.
QUESTIONS
1. Based on your experimental results, under what conditions are the charging times of different
RC circuits the same?
2. In the form V = Vo (1 – e(- t/ )), the = R C in the exponential must have units of time. Why?
Show that this is the case.
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