Laboratory 1: Using oscilloscope and resistor network
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Objective:
To introduce the control facilities of CRO, and to use CRO to measure DC and AC voltages.
To verify the Kirchhoff’s laws.
To determine the equivalent resistance of a network.
List of Apparatus:
Power supply
Input power which convert AC line voltage to DC voltage;
Multi-meter
Collect the reading of voltage or resistance;
Experimental boards
Doing the experimental;
Signal generator
Input voltage source by different frequency;
Oscilloscope
Read the waveform on the CRO screen;
Electric wires
Adjust all the apparatus which need to use.
Stop watch (Laboratory 2)
Collect the time of capacitor and inductor in charging and discharging.
Theory:
Kirchhoff’s current law(KCL):
In order have current flow, there must exist a closed circuit.
Kirchhoff’s current law states that because charge cannot be created but must be conserved, the sum of the current at a node must equal zero, i.e.
Kirchhoff’s voltage law(KVL):
Kirchhoff’s voltage law states that the net voltage around a closed circuit is zero, i.e.
Ohm’s law:
An ideal resistor is a device that exhibits linear resistance properties according to Ohm’s law, which states that V=IR.
The unit of resistance is ohm.
Ground:
The concept of reference voltage g=finds a practical use in the ground voltage of a circuit
It is a convenient to assign a potential of 0V to the ground voltage reference.
Basic of Oscilloscope(CRO):
The CRO is said to be the eyes of electronic engineers, because it is a very useful and versatile instrument to detect and measure signals in electronic circuits. Basically, the
CRO is a voltmeter and frequency meter with a high speed display mechanism. The simplified block diagram of CRO is shown in following Figure.
It can be seen from Figure 1 that the CRO will display Y inputs on the vertical axis and time-base or X input on the horizontal axis on the screen.
Energy stored in a Capacitor:
The charge o the capacitor is proportional to the voltage across it as defined by the relationship, q=CV
If the voltage across the capacitor changes with time, then q(t)=Cv(t).
The instantaneous power can be further expressed by:but
S = Complex
|S| = Apparent
Pav = Real
Q = Reactive
= V - I
Hence,
The computation of AC power is greatly simplified by using the complex power S.
oror
It can further express into:
The magnitude of S is measured in units of volt-amperes (VA) and is called apparent power.
Time Constant:
Charging Process
When t=τ,
Time constant is the time taken for the charge to rise up to around 63% of the final charge.
Discharging Process
When t=τ,
Time constant is the time taken for the charge to drop to around 37% of the initial charge.
Procedure:
Turn on the CRO.
Press CH1 button in the CRO control panel and set the time-base to 500 ms/DIV by the Time scale control knob. Adjust the line to the center of the display by using the Vertical shifting knob.
Turn the horizontal shifting knob. What do you observe?
Turn the vertical shifting knob. What do you observe?
Leave the line moves in the upper portion of screen.
Press CH2 button so that only Channel 2 is displayed and set its input to GND. Repeat steps 3 and 4 but leave the spot moves in the lower portion of screen.
Select Channel 1 and move the trace to the center of screen which is chosen as the 0 V line.
Select DC coupling by using the menu buttons at the right of the CRO display.
Connect the coaxial cable to the output terminal “channel 1” of the given DC power supply and the input terminal of the CH1 of the CRO. Increase the power supply voltage to 20 V in steps of 2 volt. At each step measure the voltage on the CRO.
Disconnect the coaxial cable from the DC power supply and connect it to the output terminal of the signal generator.
Set the signal generator to “sine wave” at frequency of 500 Hz. Adjust the amplitude to maximum. Press the Auto button so that a stationary trace on the display is obtained. Measure and record the period, frequency, maximum (peak) voltage, and peak-to-peak voltage.
Repeat step 10 with frequency set at 5 kHz, and 50 kHz. Adjust the “TIME/DIV” knob to obtain proper displays. Record the results.
Adjust the voltage of the DC power supply to 5V for channel 1 and turn off the DC power supply.
Connect the output terminal “channel 1” of the DC power supply with two wires to the BE002 experiment board where positive and negative terminals of the power supply are connected to the input and ground sockets of the experiment board respectively.
Turn on the DC power supply.
Measure the voltage across nodes A and C which should be equal to 5V roughly by using the provided multi-meter.
Measure the voltages using the multi-meter across the branches that connect to Node B.
Measure the voltage around loop AMBCA.
Repeat step 18 for the loop ABMCA.
Turn off the power of the supply and use multi-meter to measure the equivalent resistance RAC of the network shown in Figure 5 between terminals A and C. Do not remove the power supply from the circuit.
Measure again with the removal of power supply.
Result: (Figure 1.x for laboratory 1, Figure 2.x for laboratory 2)
Conclusion and discussion:
Laboratory 1:
In step 3-4:
At the beginning, the lines are in the equilibrium (Figure 1.1). When turn the horizontal shifting knob. It moves upward(Figure 1.2). When turn the vertical shifting knob. It moves leftward(Figure 1.3).
In step 5:
The CRO display is shown in here:
In step 8: (Figure 1.4 to Figure 1.13)
It shows that the CRO voltage is following the DC supply voltage.
In step 9-11: (Figure 1.14 and Figure 1.17)
In step 15: (Figure 1.18)
The measuring voltage across nodes A and C is 4.94Von the multi-meter which the DC power supply is 5.0V.
In step 16:
Using V=IR equation to calculate the current by the given resistance.
IAM + ICM + IBM=0.068571428-0.11+0.041=-0.000428572A
The Kirchhoff’s current law is not valid for both cases because the sum of current at node B and node M are not equal to 0A which is -0.0004A and 0.0003A. From the Kirchhoff’s current law, the sum of the current at a node must equal zero, i.e..
In step 18:
VAM + VMB + VBC + VCA=3.84-0.81+1.92-4.94=0.01V
VAB + VBM + VMC + VCA=3.01+0.81+1.1-4.94=-0.02V
The Kirchhoff’s voltage law is valid for both cases because the sum of voltage at loop AMBCA and loop ABMCA are not equal to 0V which is -0.02V and 0.01V. From the Kirchoff’s voltage law, the net voltage around a closed circuit is zero, i.e..
In step 20:
The resistance is 23.9Ω.
In step 21:
The resistance is 23.7Ω.
For step 20 and 21, when closing the power supply, the reading of the resistance is decreased. It is because the power supply also has resistance although the power supply is closed. Therefore, when removing the power supply, the resistance will decrease from 23.9Ω to 23.7Ω. It means the resistance of power supply is 0.2Ω.
Main Errors:
When using the experiment apparatus for a long time, the reading around the experiment will be inaccurate because of the increasing heat and resistance;
The thinner electric wire has larger resistance.
Other errors:
Experimental Errors(Laboratory 2)
Errors are uncertainties in measured quantities which arise from different sources due to:
Limitations of the observer;
These errors cause a measurement to deviate from its true value.
Systematic Errors
Systematic errors are constant greater or constantly smaller than the actual values;
Systematic errors cannot be reduced or eliminated by taking the average of repeated readings;
It could be reduced or eliminated by techniques such as calibration curves and control experiments.
Random errors produce unpredictable deviations from the true value such that each reading has equal chance to fall above or below the true value;
Examples are:
Human reaction time (Stop watch); (Laboratory 2)
Random parallax error (CRO reading);
Imperfect material used (Electric wire)
Random errors cannot be eliminated but could be reduced by taking the average of repeated readings.
Main recommendation:
When using the experiment apparatus for a long time, rest the experiment apparatus to let it cool down, then the reading around the experiment will not be inaccurate;
Using thicker electric wire to decrease the resistance.
References:
Chau, J. (2012). Lecture 2:Fundamentals of electric circuits. [Class handout]. Basic Electricity and Electronic, HKCC, POLYU
Chau, J. (2012). Lecture 5:Alternating Current(AC) network analysis. [Class handout]. Basic Electricity and Electronic, HKCC, POLYU
Chau, J. (2012). Lecture 7:AC Power. [Class handout]. Basic Electricity and Electronic, HKCC, POLYU
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