ee

Name:		Lab:	7
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Lab 7: AC Analysis of RC and RL Circuits

Objective:

After completing this exercise, you should be able to:

· Identify the primary functions and controls on a two channel oscilloscope

· Apply Kirchhoff’s Voltage Law to series AC resistive circuits

· Use the oscilloscope to measure the voltage across elements within an AC circuit.

· Construct and analyze Resistive-Inductive (RC) Circuits

· Classify resisters, capacitors, and inductors by shape, size, and part markings

Materials:

1 x	Elvis Unit with: On-Board Function Generator Prototyping board	1 x 1 x 1 x	2.7 kΩ Resistor 10 mH Inductor 0.033 uF Capacitor
1 x	2 channel Oscilloscope Tektronix TDS210 or DPO2012 or equivalent

Discussion:

Capacitors and inductors are devices that provide short term storage of energy in electrical circuits. Capacitors store energy as an electrical field while inductors store energy as a magnetic field. Because of this, current can be said to lead voltage in a capacitor because of the need for electrons to move onto the capacitor in order to build the charge that is to be stored. Further, they can be said to oppose a change in voltage because of this storage effect. This can be expressed mathematically by the equation:

Similarly, voltage can be said to lead current in an inductor because of the need to drive current through the inductor to create the magnetic field. This can be represented by the equation: Resistive-Capacitive, or RC circuit, and Resistive-Inductive (RL) circuits are circuits that contain resistive and either capacitive or inductive elements. In order to analyze these circuits, the impedance of each component must be found. The reactance of a capacitor or inductor represents the magnitude of its associated impedance and can be determined with the equation:

Because impedance is a vector quantity, a direction must also be specified. Because of the relationships expressed above, we can use Ohm’s Law to determine that the phase angle on the impedance of a capacitor is -900, while the phase angle on the impedance of an inductor is +900. As a result, the impedance of each component can be represented as:

This impedance can then be combined with other impedances in the circuit using the same approaches introduced in DC circuits to determine the total impedance of the circuit.

This lab will provide an overview of series RC and RL circuits and will demonstrate the relationship between the phase angle and the magnitude of the component values. The students will first build a series RC circuit for analysis and measurement then will repeat the activity using a series RL circuit.

Procedure:

Part 1: RC Circuits

1. Construct the circuit shown to the right. Connect channel 1 of the oscilloscope to point Va in the circuit and channel 2 to point Vb. Verify that both channels of the oscilloscope are connected to the ground reference point as indicated.

2. Set the Elvis virtual function generator to 8 Vpp with a frequency of 500 Hz. Refer to lab 5 for operation of the Elvis virtual function generator.

3. Measure the peak-to-peak value of VR. This will be represented by the voltage measured from point Vb with respect to ground. Record this value in the table below.

4. The phase angle of VR with respect to Vs can be determined using the equation

Where

t represents the time between corresponding points on the waveforms.

T represents the period of the waveforms.

Note:

The phase angle can be measured directly with the DPO-2XXX series oscilloscopes.

5. Repeat steps 2 through 4 for the remaining frequencies listed in the table below.

Frequency	VR	θR	VC	θC
500 Hz
1 kHz
2 kHz
5 kHz
10 kHz

Note:

The phase angle for the voltage on the resistor should be positive and the phase angle of the voltage on the capacitor should be negative. If this is not the case, check your calculations or oscilloscope setup.

6. Reverse the components as seen in the diagram to the right and repeat steps 1 through 5 above. This time, you are measuring VC and its phase angle relative to VS. Record the voltage measurements and phase angle calculations in the table above.

7. Use the results from the table above to sketch the voltage phasor diagrams for this circuit at frequencies of 500 Hz, 2 kHz, and 10 kHz. You can use the arrows under the Shapes menu to insert the phasors in the diagram.

8. Use the nominal resistor value along with the measured resistor voltages from the table above to determine the current in the resistor at each of the frequencies indicated. Record these values in the table below.

9. Calculate the capacitive reactance at each frequency indicated above. Use these values, along with the measured capacitor voltages from steps 1-6 to calculate the current at each of the frequencies indicated. Record these values in the table below.

Frequency	R	IR	XC	IC
500 Hz	2.7 kΩ
1 kHz	2.7 kΩ
2 kHz	2.7 kΩ
5 kHz	2.7 kΩ
10 kHz	2.7 kΩ

Questions:

1. Refer to the first table above. Describe the behavior of the circuit as the frequency increased.

2. Refer to the second table above. What happens to the current in a series RC circuit as frequency increases? Explain.

3. Refer to the second table above. How do IC and IR compare? Why?

4. Use the values of XC and R from the second table above to determine the magnitude and phase angle of the total impedance (ZT) at each of the indicated frequencies. Record these results in the table below.

Frequency
1 kHz
2 kHz
5 kHz
10 kHz
20 kHz

5. Explain the behavior of the phase angle in the table above. Is there a limiting or maximum phase angle that the total impedance can achieve? Explain.

Procedure:

Part 2: RL Circuits

1. Construct the circuit shown to the right. Connect channel 1 and channel 2 of the oscilloscope as indicated. Verify that both channels of the oscilloscope are connected to the ground reference point.

1. Set the Elvis virtual function generator to 8 Vpp with a frequency of 10 kHz. Refer to lab 5 for operation of the Elvis virtual function generator.

1. Measure the peak-to-peak value of VR. This will be represented by the voltage measured from point Vb with respect to ground. Record this value in the table below.

1. The phase angle of VR with respect to Vs can be determined using the equation

Where

t represents the time between corresponding points on the waveforms.

T represents the period of the waveforms.

1. Repeat steps 2 through 4 for the remaining frequencies listed in the table below.

Frequency	VR	θR	VL	ΘL
10 kHz
20 kHz
40 kHz
60 kHz
80 kHz

1. Reverse the components as seen in the diagram to the right and repeat steps 1 through 5 above. This time, you are measuring VL and its phase angle relative to VS. Record the voltage measurements and phase angle calculations in the table above.

1. Use the results from the table above to sketch the voltage phasor diagrams for this circuit at frequencies of 10 kHz, 40 kHz, and 80 kHz. You can use the arrows under the Shapes menu to insert the phasors in the diagram.

1. Calculate the inductive reactance at each frequency indicated above. Use these values, along with the measured inductor voltages from steps 1-6 to calculate the current at each of the frequencies indicated. Record these values in the table below.

1. Use the nominal resistor value along with the measured resistor voltages to determine the current in the resistor at each of the frequencies indicated. Record these values in the table below.

Frequency	XL	IL	R	IR
10 kHz			2.7 kΩ
20 kHz			2.7 kΩ
40 kHz			2.7 kΩ
60 kHz			2.7 kΩ
80 kHz			2.7 kΩ

Questions:

1. Refer to the first table above. Describe the behavior of the circuit as the frequency increased.

1. Refer to the second table above. What happens to the current in a series RL circuit as frequency increases? Explain.

1. Refer to the second table above. How do IL and IR compare? Why?

1. Use the values of XL and R from the second table above to determine the magnitude and phase angle of the total impedance (ZT) at each of the indicated frequencies. Record these results in the table below.

Frequency
10 kHz
20 kHz
40 kHz
60 kHz
80 kHz

1. Explain the behavior of the phase angle in the table above. Is there a limiting or maximum phase angle that the total impedance can achieve? Explain.