AC RC CIRCUIT
PURPOSE
The purpose of this lab is to show that the theoretical value of the impedance, Z, of an ac circuit element differs
by less than ±10% from the accepted value and the theoretical value of the phase shift differs by less than ±10%
from the accepted value.
THEORY
For an ac circuit, the voltage can be written as V = Vmsin( ft) and the current as I = Imsin( ft – ) where f is
the frequency in Hz and is the phase difference. The phase difference represents the time difference
between the peaks of the current and the voltage. This is usually expressed as an angle in degree mode. The
ratio of this angle to 360° represents by what fraction of the period the two peaks are separated. The phase
difference is negative if the current peaks first and positive if the voltage peaks first.
The impedance, Z, measured in ohms of an ac circuit element can be defined to be the ratio of the amplitude of
the voltage to the amplitude of the current.
Z = |Vm/Im|
Eq. 1
This equation will be used to calculate the accepted value of Z.
The theoretical value of impedance of a capacitor is called the capacitive reactance, Xc, and can be calculated
using:
Xc = 1/ ( C)
Eq. 2
where C is the capacitance and
f) is called the angular frequency. The theoretical value of the phase
angle of a capacitor is 90°. This means that the current and voltage are separated by ¼ (=| 90°/360°|) of a
period and since the angle is negative, the current peaks before the voltage.
The theoretical value of the impedance of a resistor is simply its resistance, R, and the phase angle is 0.
Z=R
Eq. 3
When a capacitor and a resistor are connected in series, the theoretical impedance of the combination can be
calculated using:
Z=
R2
XC
2
Eq 4
The theoretical phase shift for an RC circuit can be calculated (in degree mode) using:
= invtan( Xc/R).
Eq. 5
To experimentally determine , measure the time difference, ∆t, between the peak of the current graph and the
peak of the voltage graph and the following equation
∆t/T)·360°
where T is the period measured in seconds. Recall that the period is the reciprocal of frequency
Eq. 6
PROCEDURE
1. Click on the “Physics Folder” Open the file called AC-RC.
2. Record the resistance of the resistor and the capacitance of the capacitor on the data sheet.
3. Turn on the power supply. Turn the amplitude of the power supply counterclockwise to zero out the voltage. Adjust
the frequency to 50.0Hz. Click the zero button and select both probes to zero.
4. Adjust the ac voltage (turn the amplitude knob clockwise) between 3.0V and 3.5V.
5. Connect the circuit as shown in Figure 2. To do this, connect the two wires to the posts of the resistor.
6. Click the collect button to begin data collection. Two sinusoidal graphs will appear. The graphs will be for the
voltage vs. time and current vs. time. Click the “Auto Scale” button
.
7. Click on the “Experiment” Menu and select “Store latest run”. This will save your data/graph. Scroll over on your
data table and double click on the “Run 1” and rename it Resistor.
8. Take the wires from the resistor and place the wires into the leads on the capacitor (See Figure 3). Repeat steps 6-7
but replace “Run 1” with Capacitor.
9. Connect the resistor and capacitor in series (See Figure 4) and repeat steps 6-7. For step 7 replace “Run 1” with RC.
10. Left Click on the y-axis “Potential” on the Resistor graph and select “More” from the drop down menu. Unselect the
potential boxes for the Capacitor, RC, and Latest.
11. Left Click on the right y-axis “Current” on the Resistor graph and select “More” from the drop down menu. Unselect
the current boxes for the Capacitor, RC, and Latest.
12. Left Click on the y-axis “Potential” on the Capacitor graph and select “More” from the drop down menu. Unselect the
potential boxes for the Resistor, RC, and Latest.
13. Left Click on the right y-axis “Current” on the Capacitor graph and select “More” from the drop down menu. Unselect
the current boxes for the Resistor, RC, and Latest.
14. The RC graph will be on PAGE 2. The drop down box is on the upper left-hand part of the screen. Click the “Auto
Scale” button. Left Click on the y-axis “Potential” on the RC graph and select “More” from the drop down menu.
Unselect the potential boxes for the Capacitor, Resistor, and Latest.
15. Left Click on the right y-axis “Current” on the RC graph and select “More” from the drop down menu. Unselect the
current boxes for the Capacitor, Resistor, and Latest.
16. Click on the “Resistor” graph to select it.
17. Click the curve fit tool (
). This will bring up a dialog box called “Select Column for Curve fit”.
18. Select the “Resistor|Current” radio button and click “Ok”. Select the sine curve from the list of general equations and
click the “Try Fit” button. This will perform a curve fit for the selected curve. Repeat this for “Resistor|Potential”.
19. Click on the “Capacitor” graph to select it. Repeat step 17 for the “Capacitor|Current” and “Capacitor|Potential”.
20. Click on the “RC” graph to select it. Repeat step 17 for the “RC|Current” and “RC|Potential”.
21. Save your program and return to the Physics Lab. Print out these graphs.
ACRC LAB SHEET 1
DATA TABLE:
Capacitance
Resistance
CALCULATIONS: SHOW ALL WORK
1. Use equation 1 and your graphs for the resistor alone to determine the experimental value for the impedance of the
resistor. Compare the given value of the resistance of the resistor to this value.
2. Use equation 1 and your graphs for the capacitor alone to determine the experimental value for the impedance of the
capacitor.
3. Use equation 1 and your graphs for the RC circuit to determine the experimental value of the impedance for this
circuit.
4. Use equation 2 and the value of C to calculate the theoretical value of the impedance of the capacitor, XC.
5. Use equation 4 and the actual values of impedance for the capacitor and the resistor obtained in Steps 1 and 2 to
calculate the actual value of impedance for the RC circuit.
6. Compare the accepted values of the impedance obtained in Steps 1 through 3 to the theoretical values from Steps 4
through 6. Do this by calculating the % E, using: % E = 100 *|theoretical value – experimental|/|(accepted value)|.
RESULTS TABLE: SHOW ALL WORK
Expermental Impedance
R
C
RC
CONCLUSION:
TURN IN: LAB SHEET 1, ALL GRAPHS
Actual Impedance
Percent Error