Lab 5 Resistor-Capacitor Circuits
Introduction
We will examine the time dependence of the voltage and charge on the capacitor and the resistor
in series resistor-capacitor circuits.
Equipment
1 kΩ resistor, 50 nF (0.05 µF) capacitor, function generator, oscilloscope, wires and adapters of
various kinds.
Background
In a pure capacitor circuit, the capacitor charges extremely fast as there is no resistance. When a
resistor is added in series to the capacitor, the current is limited so the charging process can be
slowed to an observable rate. Here is the series resistor-capacitor circuit.
R
V
C
Q=0
R
charging
current
V
C
discharging
current
Q = Qmax
Starting with no charge on the capacitor, the voltage on the capacitor at some time, t, after
charging starts is the following function.
V(t) = Vmax (1 − e −t/τ )
The value
τ = RC
is called the time constant of the circuit. It measures the rate at which the capacitor charges and
discharges. The same exponential behavior is present during the discharging process. The
voltage across the capacitor is this.
V(t) = Voe −t/τ
Here, Vo is the voltage across the capacitor at time equals zero.
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The Resistor-Capacitor Circuit
Build the following RC circuit. Use the 0.05 µF capacitor and the 1 kΩ resistor.
R = 1 kΩ
VAC
Ch 1
C = 0.05 µF
OSC
Ch 2
Connect the output of the function generator to channel 1 of the oscilloscope, and set the function
generator output to the square wave of ±10 V at 1 kHz.
10 V
1
0V
–10 V
If the oscilloscope image is jumpy, adjust the TRIGGER LEVEL.
Connect the capacitor to channel 2 of the oscilloscope. Overlay the capacitor voltage on top of
the function generator signal. The left arrows should be aligned. The scope should look like the
plot below.
10 V
1,2
0V
–10 V
charge
discharge
charge
discharge
When the function generator switches to +10 V, it begins to charge the capacitor. Since the
resistor is there, The capacitor charges slower than the power supply. Hence, we can observe the
charging function. When the function generator drops to –10 V, the function generator discharges
the capacitor. Again, due to the resistor, the process is slowed so that the discharging process
can be observed.
Zoom in to one of the or discharge curves. If the discharge tail does not quite reach zero,
decrease the frequency slightly so that it does. Stop the updating with the RUN/STOP button.
Measure the Baselines
Use the CURSOR button to bring up the cursor menu. Set the type to cursor to AMPLITUDE. Set
the channel to CHANNEL 1. Measure the value of the voltage baseline.
Use the CURSOR button to bring up the cursor menu. Set the type to cursor to TIME. Set the
channel to CHANNEL 1. Measure the value of the time baseline.
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The cross-section between these two lines is our origin.
amplitude baseline
convert to (0 s, 0 V)
time baseline
Set the cursor type to TIME. Set the source to CH 2. Select the cursor 2. Move the cursor to
various positions on the curve and record the coordinate of that point on the curve. Select and
record the coordinates for 12 points.
convert to (0 s, 0 V)
Analysis
In order to get the time constant, we could fit an exponential curve to the data, but it is easier to
deal with a line so we will convert the data into a line. Starting from the equation that describes
this data,
V(t) = Voe −t/τ
1
lnV(t) = lnVo + ln(e −t/τ ) = lnVo − t
τ
This is the equation of a line if the natural logarithm of the voltage is plotted against the time.
1
Y = lnV0 − T
τ
The slope of this line is –1/τ. Fit a line through the data and calculate the slope, then calculate the
time constant from the slope. Use the time constant and the resistance to calculate the
capacitance of the capacitor. Include the unit of all values.
Use the DMM to measure the capacitance of the capacitor directly. What is the percent difference
between your curve measurement and the direct measurement?
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