Phasor diagram of rl parallel circuit

Lab Report

LAB EXPERIMENT INSTRUCTIONS

AC circuit analysis II

Lab # 3

RL Series and Parallel Circuits

Experiment #1: Series RL Circuits

Objectives:

After p11erforming this experiment you will be able to:

1. Compute the inductive reactance of an inductor from voltage measurement in a series RL circuit

2. Draw the impedance and voltage phasor diagram for series RL circuit.

3. Measure the phase angle in a series circuit using either of the two methods.

Materials Needed:

Resistor: 10 KΩ - 1 Piece.

Inductor: 100 mH – 1 Piece.

Summary of Theory:

When a sine wave drives a linear series circuit, the phase relationship between the current and the voltage are determined by the components in the circuit. The current and voltage are always in phase across resistors. With capacitors, the current is always leading the voltage by 90o, but for inductors, the voltage always leads the current by 90o.

Figure 3-1-1(a) illustrates a series RL circuit. The graphical representation of the phasors for this circuit is shown in Figure 3-1-1(b) and (c) respectively. As in the series RC circuit, the total impedance is obtained by adding the resistance and inductive reactance using the algebra for complex numbers. In this example, the current is 1.0 mA, and the total impedance is 5 KΩ. The current is the same in all components of a series circuit, so the current is drawn as a reference in the direction of the x-axis. If the current is multiplied by the impedance phasors, the voltage phasors are obtained and shown in Figure 3-1-(c).

image25.png

Figure 3-1-1 (a)

Procedure:

In this experiment, you learn how to make measurement of the phases angle. Actual inductors may have enough resistance to affect the phase angle in the circuit. You will use a series resistor that is large compared to the inductor’s resistance to avoid this error.

1. Measure the actual resistance of a 10 KΩ resistor and the inductance of a 100 mH inductor. If the inductor cannot be measured, record the listed value. Record the measured values in Table 3-1-1.

2. Connect the circuit shown in Fig 3-1-2. Set the generator voltage with the circuit connected to 3.0 VPP at a frequency of 25 KHz. The generator should have no dc offset. Measure the generator voltage and frequency with oscilloscope as many meters cannot respond to 25 KHz frequency. Use peak-to-peak readings for all the voltage and current measurements in this experiment.

image1.png

Figure 3-1-1 (b)

image24.png

Figure 3-1-1 (c)

Component

Listed Value

Measured Value

L1

100 mH

R1

10 KΩ

Table 3-1-1

image2.png

Figure 3-1-2

3. Using a two-channel oscilloscope, measure the peak-to-peak voltage across the resistor (VR) and the peak-to-peak voltage across the inductor (VL)

(see Fig. 3-1-3). Measure the voltage across the inductor using the difference technique described in experiment #2 of the Lab # 1. Record the voltage reading in Table 3-1-2.

VR

VL

I

XL

ZT

Table 3-1-2

4. Compute the peak-to-peak current in the circuit by applying Ohm’s Law to the resistor. That is

image3.wmf
R

V

I

R

=

Enter the computed current in Table 3-1-2.

5. Compute the inductive reactance, XL by applying Ohm’s Law to the inductor. The reactance is

image4.wmf
L

L

V

X

I

=

Enter Computed reactance in Table 3-1-2.
6. Calculate the total impedance (ZT) by applying Ohm’s Law to the entire circuit. Use the generator voltage set in step 2 (VS) and the current determined in step 4. Enter the computed impedance in Table 3-1-2.

7. Using the values listed in Table 3-1-1 and 3-1-2 draw the impedance phasors on the Plot 3-1-1(a) and the voltage phasors on the Plot 3-1-1(b) for the circuit at a frequency of 25 KHz.

image5.png

Plot 3-1-1

8. Compute the phase angle between VR and VS using trigonometric relation.

image6.wmf
1

L

R

V

Tan

V

q

-

æö

=

ç÷

èø

Enter the computed phase angle in Table 3-1-3.
9. Two methods for measuring phase angle will be used. The first method can be used with any oscilloscope. The second can only be used with oscilloscopes that have a “fine” or variable SEC/DIV control. Measure the phase angle between VR and VS using one or both methods. The measured phase angle will be recorded in Table 3-1-3.

Phase Angle Measurement: Method #1:

a) Connect the oscilloscope so that the channel 1 is across the generator and channel 2 is across the resistor. [See Fig 3-1-3]. Obtain a stable display showing between one and two cycles while viewing channel 1 (VS). The scope should be triggered from channel 1.

b) Measure the period T of the signal from the generator. Record it in Table 3-1-3. You will use this time, T, in step (e).

image7.png

Figure 3-1-3

c) Set the oscilloscope to view both channels. Do not have channel 2 inverted. Adjust the amplitude of the signals using the VOLTS/DIV, VERT POSITION, and vernier controls until both channels appear to have the same amplitude as seen on the scope face.

d) Spread the signal horizontally using the SEC/DIV control until both signals are just visible across the screen. The SEC/DIV control must remain calibrated. Measure the time between the two signals,

image8.wmf
t

D

, by counting the number of divisions along a horizontal graticule of the oscilloscope and multiplying the SEC/DIV setting. (See Fig. 3-1-4). Record the measured
image9.wmf
t

D

in Table 3-1-3.
e) The phase angle may now be computed from the equation.

image10.wmf
360

t

T

q

D

æö

=´°

ç÷

èø

Enter the measured phase angle in Table 3-1-3 under the phase angle – method 1.

Computed Phase Angle

image11.wmf
q

Measured Period

image12.wmf
T

Time Difference

image13.wmf
t

D

Phase Angle

Method 1

image14.wmf
q

Method 2

image15.wmf
q

Table 3-1-3

image16.png

Figure 3-1-4

Phase Angle Measurement – Method #2:

a) In this method the oscilloscope face will represent degrees, and the phase angle can be measured directly. The probes are connected as before. View channel 1 and obtain a stable display. Then adjust the SEC/DIV control and its vernier until you have exactly one cycle across the scope face. This is equivalent to 360o in 10 divisions, so each division is worth 36o.

b) Now switch the scope to view both channels. As before, adjust the amplitude of the signals using the VOLTS/DIV, VERT POSITION and vernier control until both channels appear to have the same amplitude.

c) Measure the number of divisions between the signals and multiply by 36o per division. Record the measured phase angle in Table 3-1-3 under phase angle-method 2.

Experiment #2: Parallel RL circuits:

Objectives:

After performing this experiment, you will be able to:

1. Determine the current phasor diagram for a parallel RL circuit.

2. Measure the phase angle between the current voltage for a parallel RL circuit.

3. Explain how an actual circuit differs from the ideal model of a circuit.

Materials Needed:

Resistors: 3.3 KΩ - 1 Piece, 47Ω - 2 Pieces.

Inductor: 100 mH – 1 Piece.

Summary of Theory:

In a parallel RL circuit, the current phasors will be drawn with reference to the voltage phasor. The direction of the current phasor in a resistor is always in direction of the voltage. Since current lags the voltage in an inductor, the current phasor is drawn at an angle of – 90o from the voltage reference. A parallel RL circuit and the associated phasors are shown in Figure 3-2-1.

image17.jpg

Figure 3-2-1

The practical inductors contain resistance that frequently is large enough to affect the purely reactive inductor phasor drawn in Figure 3-2-1. The resistance of an inductor can be thought of as a resistor in series with a pure inductor. The effect on the phasor diagram is to reduce an angle between IL and IR. In a practical circuit, this angle will be slightly less than the -90o shown in the Figure 3-2-1. This experiment illustrates the difference between the approximations of circuit performance based on ideal components and the actual measured values.

Recalling the previous experiment – RL series circuit, the phase angle between the source voltage, VS, and the resistor voltage, VR in a series circuit were measured. The oscilloscope is a voltage-sensitive device, so comparing these voltages is straightforward. In parallel circuits, the phase angle of interest is usually between the total current, IT, and one of the branch currents. To use the oscilloscope to measure the phase angle in a parallel circuit, we must convert the current to a voltage. This was done by inserting a small resistor in the branch where the current is to be measured. The resistor must be small enough not to have a major effect on the circuit.

Procedure:

1. Measure the actual resistance of a resistor with a color-code value of 3.3 KΩ and resistance of two current-sensing resistors of 47Ω each. Measure the inductance of a 100 mH inductor. Use the listed value if you cannot measure the inductor. Record the measured values in Table 3-2-1.

2. Measure the winding resistance of the inductor, RW , with an ohmmeter. Record the resistance in Table 3-2-1.

3. Construct the circuit shown in Figure 3-2-2. Notice that the reference ground connection is at the low side of the generator. This connection will enable you to use a generator that does not have a “floating” common connection. Using your oscilloscope, set the generator to a voltage of 6.0 VPP at 5 KHZ. Check both the voltage and frequency with your oscilloscope. Record all voltages and currents in this experiment as peak-to-peak values.

image18.png

Table 3-2-1

image19.png

Figure 3-2-2

4. Using the oscilloscope, measure the peak-to-peak voltages across R1, RS1 and RS2. Use the two channel difference method (described in Lab#1) to measure the voltage across the two ungrounded resistors. Apply Ohm’s Law to Compute the Current in each branch. Record the measured voltage drops and the computed currents in Table 3-2-1. Since L1 is in series with RS2, enter the same current for both.

5. Using the computed peak-to-peak currents from Table 3-2-1, draw the current phasors for the circuit on the Plot 3-2-1. [Ignore the effects of the sense resistors].

image20.png

Plot 3-2-1.

image21.wmf
1

L

R

I

Tan

I

q

-

æö

ç÷

ç÷

èø

=

Phase Angle

Between

Computed

Measured

IT and IR

IR and IL

90o

IT and IL

Table 3-2-2

6. The phasor diagram illustrates the relationship between the total current and the current in each branch. Using the measured currents, compute the phase angle between the total current (IT) and the current in R1 (IR). Then compute the phase angle between the total current (IT) and the current in L1 (IL). Enter the computed phase angles in Table 3-2-2 (Note that the computed angles should add up to 90o, the angle between IR and IL.

7. In this step, you will measure the phase angle between the generator voltage and current. This angle is approximately equal to the angle between IT and IR as show in Figure 3-2-1. (Why?). Connect the oscilloscope probes as shown in Figure 3-2-3. Measure the phase angle using one of the methods in the previous experiment. The signal amplitudes in each channel are quite different, so the vertical sensitivity controls should be adjusted to make each signal appear to have the same amplitude on the scope. Record the measured angle between IT and IR in Table 3-2-2.

image22.jpg

Figure 3-2-3

8. Replace RS1 with jumper. This procedure enables you to the reference the low side of R1 and RS2. Measure the angle between IL and IR by connecting the probes as shown in Fig 3-2-4. Ideally this measurement should be 90o, but because of the coil resistance, you will likely find a smaller value. Adjust both channels for the same apparent amplitude on the scope face. Record your measured result in the second line in the Table 3-2-2.

image23.png

Figure 3-2-4

9. By subtracting the angle measured in step 7 from the angle measured step 8, you can find the phase angle between IT and IL. Record this as the measured value on the third line of the Table 3-2-2.

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