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Electric Circuits lab EE 213 Biomedical Engineering Department

Experiments. (1A),(1B)

INTRODUCTION TO BASIC LABORATORY TEST AND MEASUREMENT

EQUIPMENT

Part A: 1 The DC Power Supply: This is a dual power supply with (+) and (-) voltage terminals, and a ground (common) terminal. dual-output laboratory power supplies voltage and current are indicated on three-digit display case closed at top and bottom can be operated in parallel or in series , can be operated as constant voltage source or as constant current source voltage and current are adjustable from 0 up to the rated value The main attributes of this device is: *Voltage and current are indicated on separate LED-meters. *The output voltages are available through safety sockets on the front panel. *Dual Tracking (Serial and parallel operation) Both lab-outputs can be connected in parallel or in series by means of a switch on the front panel. The left hand unit is then operating as the master control unit. *The output values are indicated on the meters of the master unit (left side). *The units are equipped with a third output supplying a fixed voltage of 3...6 Volts and a max. Current o f 2 A. This output is located on the right side with safety sockets. *out put on/off switch.(see figure 1)

Figure 1:- The Dc power supply

Before performing the following procedure; mark various controls and meters: 1- Apply input power. 2- Turn the current limit control to Max (clock wise) 3- Select the voltage meter; record in indicated value……………………. 4- Select the current meter. 5- Place (S.C) between (+) & (-) output terminals. 6- Turn the voltage control slowly up until maximum voltage is indicated, 7- Then record this value…………………………………………………..

Q1: Does the current value change when the voltage controls are turned up any further. ……………………………………………………………………………… (Disconnect the S.C)

8-Select the voltage meter. 9-Record its reading 10- Select the current meter. 11- Turn the current limit control down (counter clock wise). 12- Then record the value of voltage meter……………………………………..

Q2: Does this value of voltage meter change when the current control turned up any further. ……………………………………………………………………………… 2-The Digital Multimeter:

Most digital multi meters are designed to measure: 1. DC resistor. 2. Direct current and voltage. 3 .rms value of sinusoidal current and voltage.(see Figure 2)

• Some meters measure True rms (TRMS) value of a waveform.

Figure 2: The Digital Multimeter

(A) Resistance Measurements: 1-Obtain a resistance. 2-Prepare the DMM for resistance (Ω) measurements. 3-Connect the DMM probes to the two terminals of the resistor. 4-Select the DMM auto range and record its reading. 5- Repeat with the smallest range setting. *Also you can measure (B) Direct Current Measurements.

(C) Alternating Current Measurements. (D) Direct Voltage Measurements. (E) Alternating-voltage measurements. 3-Project Board A breadboard (protoboard) is a construction base for prototyping of electronics Because the solderless breadboard does not require soldering, it is reusable. This makes it easy to use for creating temporary prototypes and experimenting with circuit design.( see figure 3 )

Figure 3:-Example breadboard drawing.

PART B: 1-THE Oscilloscope: This is one of the most important laboratory test equipment It is basically a voltage sending and display device. Scopes have 2 inputs channels with adjustable, calibrated, gain. 2 signals can be viewed separately or simultaneously.(see figure 4) Horizontal time axis is provided by internal generator; thus, a voltage waveform applied to either input channel can be viewed as a function of time. Another important Scope function is the Trigger. Finally there are controls, which affect the Quality of the display: *A focus control adjusts the sharpness of the displayed image. *An intensity control adjusts its brightness.

Make a neat sketch of the front panel of the scope and mark the basic information:

Figure 4:-The Oscilloscope

2- Function Generator

Figure 5: Function generator

1-Turn the power on. 2-Turn DC offset to OFF. 3- Symmetry to Normal. 4- Set frequency to 1000 Hz. 5- Set the function Selector to sinusoidal output. 6- Set the amplitude to Max value. 7- Measure the rms value of the output with DMM. 8- Set the output amplitude to Min. 9 -Measure the output with DMM. 3-electrical connector 1-The BNC connector (Bayonet Neill–Concelman) see figure 6

Figure 6: Oscilloscope probe BNC - double clips (crocodile) and BNC-BNC Wires respectively.

2- Banana connectors. (See figure 7)

Figure 7: Banana plug to Banana plug wire

3- Banana Plug to Alligator (crocodile) Clip wire. (See figure 8)

Figure 8: Banana to crocodile connector


LAB SHEET 1

Experiment 2

Resistors, potentiometers, and rheostats

Resistance Measurements: Several methods will be used to measure resistance. Their results will be compared with each other and with nominal color-code value.

1-obtain two resistors having arbitrary values between 100 ohms and 100 K ohms and arbitrary power ratings.

2-Tabulate their color codes, nominal values, percent tolerances, and power ratings.

(A) Ohmmeter Measurements: 1-Use the DMM to measure the value of each resistor directly on the most sensitive range. R1 (measured)…………………………………………….. R2 (measured) ……………………………………………. 2-Compare with the nominal values. 3-As an aside, measure and record your body resistance by holding the probes firmly. One with each hand ………………………………….. (B) Voltage and Current Measurements: Construct a measurement circuit as shown in the figure 1, where Rx is the resistance to be determined by Ohm’s law:

Color-code Nominal value Tolerance Power rating

(R1) Brown-black-brown -Gold

(R2) Red-red-red-Gold

Rx=Vx/Ix.

Figure 1

1- Set each DMM to the highest possible range. 2- Increase Vs from 0 to near the highest responsible value. (Within limits that are safe for the resistor Rx ) .(See the table below).

Vs (V) 3 5 10 Ix Vx

Rx=Vx/Ix 3- Decrease the range setting of each DMM steps. 4- Record the measure value of Vx, Ix. 5-Calculate the value of Rx by the Ohm’s law.

(C) Bridge Measurements: A Wheatstone bridge for measuring resistance is shown in Figure 2. When the Bridge is balanced, i.e.,Ib=0,

Figure 2 The following relation holds:

Rx=R2*R3/R1

*Derive this formula in your report. *Generally, a good measurement is obtained when all Resistors values are not too far from each other; for example, within a factor of 3 or less. 1-Select reasonable values for R1and R2, and measure them with the DMM before placing them in the Circuit. 2- Use decade box for the adjustable resistor R3.Use approximately 10 V for Vs. 3- Set the DMM initially to the highest Current range. As you adjust R3 to make Ib approach 0, increase the DMM sensitivity. Stop adjusting when a minimum value of Ib is obtained on the lowest possible range. Record this value for reference only. 4- Disconnect R3 and measure it directly with the DMM……………………….. 5-Calculate the value of unknown Rx using above formula. 6- Compare with the nominal values. Potentiometers Two popular shapes of Potentiometers are: 1-Circular 2-Straight lines Potentiometers are used as a:- 1) Voltage current device. 2) Current control device.

Rheostat: A rheostat is similar to a Potentiometer in structure. However, it differs in its intended use it is used as a series element to control Current as shown in figure 3. Thus, it is usually a higher-power device .To demonstrate its principle, one of the Potentiometer you tested may be used in the following measurements.

Figure 4

Rheostat Measurements: For the circuit shown in the figure 4. Obtain a Potentiometer, Select Ro such that the maximum variation in the Current Io is 5 to 1.Measure and record the value of Ro. Construct the circuit using 10 v for vs. starting at safe DMM current range measure Io on the lowest possible range using the 4 marked sections of the potentiometer for Rs, i.e, 0,25,50,75.and 100 percent. Plot Io Vs Rs.what functional relation does this plot indicates.

Rs (KΩ ) Io

5

4

3

2

1


Post lab #1

Experiment 2

Resistors, potentiometers, and rheostat

1. Student Name ………………………………………………………………………

Student ID…………………………………………………………………………..

2. Student Name ………………………………………………………………………

Student ID…………………………………………………………………………..

3. Student Name ………………………………………………………………………

Student ID…………………………………………………………………………..

Resistance Measurements:

(A) Ohmmeter Measurements:

(B) Voltage and Current Measurements :( Ohm’s law)

Vs (V) 3 5 10

Ix

Vx

Rx=Vx/Ix

*Plot Ix vs Vx

Color-code Nominal value Tolerance Power

rating

Brown-black-brown –Gold

Red-red-red-Gold

Color-code Nominal value Measured

value

(DMM)

Tolerance Power

rating

Brown-black-brown –Gold

Red-red-red-Gold

Your body resistance is …………………………………………………………

Rx=Vx/Ix.

(C) Bridge Measurements:

Rx=R2*R3/R1 ………………….only when Ib=0

*Derive this formula:-

-Calculate the value of unknown Rx using above formula, Compare with the nominal values.

Rheostat Measurements: Plot Io Vs Rs.what functional relation does this plot indicates.

Rs (KΩ ) Io

5

4

3

2

1

• Write a small paragraph which discuss your results and give your Conclusion about all parts of this experiment ……………….……………… • ................................................................................................... ...........................

............................................................................................................. ............................. ............................................................................................................ .............................. ............................................................................................................. ............................. ............................................................................................................. ............................


LAB SHEET 2

Experiment 3A

Dc CIRCUIT MEASUREMENT PART A

aPART ONE:-Series Circuits Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed path is zero.

• Use R1=330 Ω,R2=1 K Ω,R3=2.2K Ω, then connect the circuit in Figure 1

Figure 1

1. Use DMM1 as an ammeter. 2. Use DMM2 as a voltmeter. Measure Is………………………………………. Note: Always start at the highest meter range. Move the connection of DMM2 around the circuit to measure the voltages:

Disconnect the power supply from the circuit, and use DMM2 as an

ohmmeter to measure the resistances values; (you need to use the measured values of resistances and Vs to calculate the different voltages, and compare the results with the measured values of these voltages.)

Vs/Parameter Name

Vab Vbc Vcd Vde Is

Vs=15V

Parallel Circuits: Kirchhoff's Current Law (KCL) states that the sum of all currents at any node in a circuit is zero.

Construct the circuit shown in figure 2 below with the given values:

Figure 2 Now, adjust Vs until DMM1 reads Vs=15 V, then measure the value of Is

as indicated by DMM2, Is=………………………………………………..

Now place DMM2 in series with R1, R2, and R3 to measure the values of the different currents:

Vs/Parameter Name

I1 I2 I3

Vs=15V

Disconnect the power supply, and use DMM1 as an Ohmmeter to measure

the parallel combination of R1, R2, and R3, then measure each resistance separately, ( you need to use the measured values of resistances and Vs to

Resistance name Measured Values R1 R2 R3 Is

calculate the different currents, and compare the results with the measured values of these currents.)

Series-Parallel Circuits:

Both KVL and KCL are now verified by measurements in a rather arbitrary circuit containing series and parallel combinations of resistors.

• Construct the circuit shown in figure 3, with the given values

Figure 3

Now, Use DMM as a voltmeter to measure Vs while you adjust its value to 25V,then measure the different voltages across the individual resistors, as indicated:

Voltage Measured values

Vs V1 V2 V3 V4 V5 V6

Now use the DMM as an ammeter to measure the different currents across the resistors, as below:

Current DMM value I1 I2 I3 I4 I5 I6

Use the DMM as an Ohmmeter to measure the different resistances, as

below:

Resistance name Measured value

R1 R2 R3 R4 R5 R6

Now, use the measured values of voltages to verify KVL on all closed paths, and use the measured values of currents to verify KCL at all nodes. Finally, use the measured values of resistances with Ohm's law to calculate voltages using measured currents and vice versa, then compare all the measured quantities.


Post lab #2

Experiment 3A

DC CIRCUIT MEASUREMENTS PART A

1. Student Name ……………………………………………………………………… Student ID………………………………………………………………………….. 2. Student Name ……………………………………………………………………… Student ID………………………………………………………………………….. 3. Student Name ……………………………………………………………………… Student ID…………………………………………………………………………..

PART ONE:-Series Circuits After connect the circuit in figure 1 fill the table below and answer the following questions:

Vs/Parameter Name

Vab Vbc Vcd Vde Is

Vs=15V

Compare the sum of these voltages to Vs??

Calculate the value of Vab as a percentage of Vs?? What does this mean? Vab/Vs=………………………………………

Use the above values and the measured value of Is to calculate different voltages by Ohm's law, and compare them with the values obtained previously.

Voltage name Previous value Calculated values using

Ohm's law Vbc Vcd Vde

Now, use voltage division to calculate different voltages, and compare

your results with the measured values.

Voltage name Calculated value Measured value Vbc Vcd Vde

Resistance name Measured Values R1 R2 R3

Parallel Circuits: After connect the circuit in figure 2 fill the table below and answer the following questions:

Vs/Parameter Name

I1 I2 I3

Vs=15V

measure the value of Is as indicated by DMM2

Is=………………………………………………..

compare the sum of the above currents with Is?

A Consequence of KCL is that the current through one conductance Gk =1/Rk in a parallel circuit can be calculated using the current division Rule , Ik = (Gk /Gt ) It Gt: the sum of all conductances in parallel, including Gk It: the current in to the circuit Calculate I1, I2, and I3 using this rule, and compare the results with the measured values.

Series-Parallel Circuits: After connect the circuit in Figure 3 record the following results:-

Voltage Measured values Vs V1 V2 V3 V4 V5 V6

Current DMM value I1 I2 I3 I4 I5 I6

Resistance name Measured value R1 R2 R3 R4 R5 R6

Now, use the measured values of voltages to verify KVL on all closed paths, and use the measured values of currents to verify KCL at all nodes. Finally, use the measured values of resistances with Ohm's law to calculate voltages using measured currents and vice versa, then compare all the measured quantities.

• Write a small paragraph which discuss your results and give your conclusion about all parts of this experiment ……………….………………

• ....................................................................................................................

............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................


LAB SHEET 3

Experiment 3B

DC CIRCUIT MEASUREMENTS

• PART ONE:- Measure the I-V chars of a DC power supply limited by a current (Imax).

- Set the Coarse and Fine voltage controls and the Current Limit control to

minimum. o Set, and adjust the Current Limit control in your power supply to (Imax or Is.c = 125 mA.) By connect short circuit between (+) and (–) terminals. o Disconnect the short circuit, adjust the power supply for Vso = 10V. o Connect the circuit shown in figure 1 use decade box for R1 .

R1 (Ω) ∞ 400 200 100 80 50 20 0 DMM1 (V)

DMM2 (mA) - Readjust current limit to Imax = 80 mA - Remove R1, adjust the power supply for Vso = 16V.

R1 (Ω) ∞ 1000 500 300 200 100 50 0 DMM1 (V)

DMM2 (mA)

Figure 1 PART ONE:- Ammeter Loading Note use the bench top multimeter (M 9803 R ) to measure current 1. Turn both power supply voltage to Min. 2. Construct the circuit shown in figure 2. 3. Choose R=2.2K 4. Measure R Using DMM.

Figure 2 5. Adjust Voltage Source of 4 V on DMM1. 6. Record Current by DMM2.Using lowest range. 7. Move DMM1 to measure: Va =………………………………. Vr =………………………………

Ammeter Range (A)

4m 40m 400m

Calculate ra (Ω) Va/I

PART ONE:- Voltmeter Loading Note use the bench top multimeter (M 9803 R ) to measure voltage Measurements are now made to determine the equivalent resistance of the DMM when used at voltmeter, and how it affects the accuracy of results: 1. Construct the Circuit shown in Figure 3,R1= 470KΩ; R2 = 1 MΩ , Vs = 30 V.

I=………….

Figure 3

2. Record DMM Mode number…………………………………………………….. 3. Measure V2 using lowest possible range. 4. Calculate the equivalent resistance of the DMM using the measured values of R1 and R2..

Hint Assume: (Req//R2)=R

(R/(R+R1))*Vs=V2 PART TWO Oscilloscope equivalent resistance:-

Figure 4

1. Construct the Circuit shown in figure 4. 2. Use Decade box for R2. 3. Use R1 = 1MΩ. R1 measured…………………………………………………………… 4. Set the function generator frequency to 1 KHz sine wave 8Vp-p then connect it to CH1 of the scope. 5. Connect CH2 with the voltage o/p at R2 set the scope DC coupling. Measure Vout:

R2 R2 measured By DMM Vout 50 KΩ 1MΩ 2 MΩ 5 MΩ

You need to use the above results to calculate the equivalent Scope input resistance Rin using the measured values of R1 and R2. Function generator equivalent resistance:

Figure 5

1. Construct the circuit shown in figure 5 (use decade box for RL 2. Set the function generator frequency to 100 KHz sine wave With 1Vrms (Apply the o/p of function generator to the DMM, AC measurements). 3. Measure Vo for different values of RL.

RL Vout (rms) 10 KΩ 1 KΩ 500Ω 200Ω 75 Ω 50 Ω

4. Change the frequency of function generator but keep its amplitude constant Then measure Vo

Frequency Value Vout (rms) ƒ = 1 KHz ƒ =10 KHz ƒ= 100 KHz ƒ = 1 MHz

You need to use the above results to calculate the equivalent resistance of the FG At 10 KHz frequency.


Post lab #3

Experiment 3B

DC CIRCUIT MEASUREMENTS PART B


PART ONE:- Ammeter Loading Measure R Using DMM…………………………………………………….. Record Current By DMM2.Using lowest range. Move DMM1 to measure: Va =………………………………. Vr =………………………………

Ammeter Range (A)

4m 40m 400m

Calculate ra (Ω) Va/I

Write your observations:- ………………………………………………………………………………………… …………………………………………………………………………………………

-:Voltmeter Loading Calculate the equivalent resistance of the DMM using the measured values of R1 and R2.. How does this value affect the accuracy of experimental results?:-

Hint Assume: (Req//R2)=R (R/(R+R1))*Vs=V2

I=………….

PART TWO Oscilloscope equivalent resistance:- R1 measured…………………………………………………………… Measure Vout: R2 R2 measured By DMM Vout 50 KΩ 1MΩ 2 MΩ 3.3 MΩ use the above results to calculate the equivalent Scope input resistance Rin using the measured values of R1 and R2 . Hint (the same equation as voltmeter) Function generator equivalent resistance:

RL Vout (rms) 10 KΩ 1 KΩ 500Ω 200Ω 75 Ω 50 Ω

Frequency Value Vout (rms) F = 1 KHz F =10 KHz F = 100 KHz F = 1 MHz

-What is the difference between rms value and Vo p-p?

Use the above results to calculate the equivalent resistance of the FG At 10 KHz frequency?-

• Write a small paragraph to discuss your results then give your Conclusion about all parts of this experiment ……………….……………… • ...................................................................................................

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LAB SHEET 4

Experiment 4

DC CIRCUIT ANALYSIS

• PART ONE MESH AND NODAL ANALYSIS: Mesh and nodal equations are proved using experimental data. Figure 1 shown the circuit used for this purpose.

1-Measure the actual resistance values used with DMM. 2- Use a nominal 150Ω for RL. 3-Adjust the 2 out puts of the dual power supply to 16-v & 24-v using DMM

DC voltage Measured Value 16 v 24 v

4- Measure the currents I1, I2, and I3using DMM on the lowest possible range. Similarly, use another DMM to measure the node voltage Va, Vb.

Current Measured Value I1 I2 I3

Voltage Measured Value

Va Vb

Superposition Principle: The circuit in the figure 1 is also used to verify the superposition principle using the following procedure. 1-Replace the 24-v source with S.C, but leave the 16-vsource applied measure the mesh current and voltages:

Current Measured value I’1 I’2 I’3


V’a V’b

Replace the 16-v source with S.C, but leave the 24-vsource applied measure the mesh current and voltages:

Current Measured value I’’1 I’’2 I’’3


V’’a V’’b

Thevenin Equivalent & Maximum Power Transfer: Again the circuit of Figure 1 will be used to verify Thevenin’s and the maximum power transfer theorems. Different methods will be used to determine this: 1-With 16-v and 24-v sources applied, remove RL and measure the open-circuit voltage Vao (O.C) this is the equivalent voltage Vth . 2- Measure the S.C current Iao. 3-Replace both voltage sources with S.C and measure the Thevenin Equivalent resistance RTH Between node a and the reference node.

Voltage Measured Value Vth

Current Measured Value

Iao

Resistance Measured Value RTH

Calculate the Thevenin equivalent circuit using the measured values of the 4 resistors in Figure 1 and 16-v and 24-v. Determine the Experimental values for RTH : Vao (O.C) / I ao (S.C) = -Use the Decade box for RL in figure 1. -Measure the voltage VL across RL. -Using DMM on the lowest range for:

Resistance Voltage Power 200 Ω 300 Ω 400 Ω 500 Ω 600 Ω 800 Ω 1000 Ω 1500 Ω

Calculate the power: PL = (VL)2 / RL Plot PL & VL Vs RL: Plot (v,p) From the plot determine the value Rmp of RL where PL is the Maximum Find the Corresponding value Vmp of VL: Difference RTH = Rmp

Difference VTH / 2 = Vmp

Source Transformations:

Connect the circuit below

Set the short circuit current limit on each supply to about 200mA, And then set the open circuit voltages Vs1 = 20V and Vs2 = 10V. Construct the above circuit using 2-Watt resistors R1 = 330Ω and R2 = 100Ω. And use a decade box for Ro. Now use two DMM to measure Vo and Io for different values of Ro

Ro Measured Vo Measured Io 0 Ω

20 Ω 50 Ω 100 Ω 200 Ω 500 Ω 1 K Ω 5 K Ω

IS1 = VS1 / R1 = IS2 = VS2 / R2 = Ise = Is1 + Is2

For Ise use a short-circuit-current limited supply set the open-circuit voltage of the power supply to a value slightly above say 10% above, the value Ise.[R1.R2/(R1+R2)], the value is:

Req = R1//R2 = R1R2/(R1 + R2) Vse = Ise * Req Vse +10% Vse

Now measure Vo and Io for this circuit, for the values of Ro as shown in the following table.

Ro Measured Vo Measured Io

0 Ω 20 Ω

50 Ω

100 Ω

200 Ω

500 Ω

1 K Ω

5 K Ω

We now construct the equivalent (transformed) circuit shown below with one voltage source.

set the open-circuit output voltage to the value Ise.[R1.R2/(R1+R2)] exactly, the value is: ………………………………………………

With Vse calculated from previous part Vse = 12, measure Vo and Io for this circuit, for the values of Ro as shown in the following table. Ro (Ω) 0 20 50 100 200 500 1000 5000 Vo (V)

Io (mA)

By comparing the results of the three experiments we can see that the values are equal with small differences. So we can simplify the circuit by transforming it into another form to simplify the measurements and calculations.


Post lab #4

Experiment 4

DC CIRCUIT ANALYSIS


PART ONE:- Mesh and Nodal analysis:

DC voltage Measured Value 16 v 24 v

Measure the currents I1, I2, and I3using DMM on the lowest possible range. Similarly, use another DMM to measure the node voltage Va, Vb.

Current Calculated Measured Value

Difference

I1 I2 I3

Voltage Calculated Measured

Value Difference

Va Vb

Superposition Principle: Replace the 24-v source with S.C, but leave the 16-vsource applied measure the mesh current and voltages:

Current Measured value I’1 I’2 I’3


V’a V’b

Replace the 16-v source with S.C, but leave the 24-vsource applied measure the mesh current and voltages:

Current Measured value I’’1 I’’2 I’’3


V’’a V’’b

Compare each of the sum with original values (I’1 + I’’1 = I1) …………….I2,I3 Thevenin Equivalent & Maximum Power Transfer:

Voltage Measured Value Vth

Current Measured Value

Iao

Resistance Measured Value RTH

Determine the Experimental values for RTH : Vao (O.C) / I ao (S.C) =

Resistance (RL) Voltage Power ( PL = (VL )2 / RL )

200 Ω 300 Ω 400 Ω 500 Ω 600 Ω 800 Ω 1000 Ω 1500 Ω

Plot P & VL Vs RL:

From the plot determine the value Rmp of RL where PL is the Maximum

Find the Corresponding value Vmp of VL Difference RTH = Rmp

Difference VTH / 2 Vmp

Source Transformations:

Ro Measured Vo Measured Io 0 Ω

20 Ω 50 Ω 100 Ω 200 Ω 500 Ω 1 K Ω 5 K Ω

IS1 = VS1 / R1 = IS2 = VS2 / R2 = Ise = Is1 + Is2 Ise.[R1.R2/(R1+R2)], the value is:

Req = R1//R2 = R1R2/(R1 + R2) Vse = Ise * Req Vse +10% Vse

Ro Measured Vo Measured Io 0 Ω 20 Ω

50 Ω

100 Ω

200 Ω

500 Ω

1 K Ω

5 K Ω

set the open-circuit output voltage to the value Ise.[R1.R2/(R1+R2)] exactly, the value is: ………………………………………………

Ro (Ω) 0 20 50 100 200 500 1000 5000 Vo (V)

Io (mA)

• Write a small paragraph to discuss your results then give your Conclusion about all parts of this experiment ……………….………………

• ....................................................................................................................

.............................................................................................................

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LAB SHEET 5

Experiment 5A

INDUCTANCE, CAPACITANCE I-V RELATION AND TRANSIENTS IN RLAND RCCIRCUITS

Inductor Test:

1- Obtain the inductor decade box Use DMM to measure the DC resistance RL at

400-mH setting.

2- Construct the circuit shown in figure 1 Where Vs is 4-Vp-p, 2-KHz square wave

Rs = 50 Ω.

Figure 1

RL (measured) = Rs = 50Ω L = 400 mH

Period of input Vs( t ) (T )=( 1/F )= ………………………….

3- Display the FG output voltage V1 and V2 across Rs Make an accurate sketch

of both signals showing values of time and amplitude.

4- Calculate (L / RL ) and compare with ( T/ 2 ) Where T is the period of input

Vs( t ).

Capacitor Test: 1- Obtain a capacitor decade box and use a DMM to measure the DC resistance

RC, at the 0.02 µF setting.

2- Construct the circuit shown in the figure 2 Where Vs is 8 Vp-p 200-Hz

Triangular wave Rs = 500 Ω.

Figure 2

3- Display the FG output voltage V1 and V2 across Rs together, uses DC coupling

on both scope channels. 4- Sketch V1 & V2 showing values of time and amplitude.

RL & RC Circuit Transients:

Circuit Transient Tests:-RL

+

-

Vs1

10V

L1

VL

R1

VR

Figure 3

1- Construct the RL circuit of figure 3, using R= 1 K ohm’s L = 1 H.

2- Measure the dc resistance of the inductor and the actual value of R with an

Ohmmeter.

3- Instead of the step input voltage, use a 100-Hz symmetrical square wave from the

FG. 4- Adjust the open circuit level to 4 Vp-p .

5- Remember to record the 50-ohm’s source resistance of the FG found in previous

Experiment .

6- Connect the Oscilloscope to measure VL (t). See figure 4

Figure 4: RL and RC Transient response

7- Expand the time scale to make an accurate measurement of using the 63% change

Criterion.

Record the measured value…………………………………………………….

8- Exchange the positions of R and L in the circuit to enable the display of VR By

Using a common ground between the scope and FG.

RC transient Tests:

C1

VC

+

-

Vs1

10V

R1

VR

Figure 5

1- For the RC circuit shown in Fig 5. replace the step input with the same square

wave used on the RL circuit.

2- Select R = 100 K Ω and C= 10 nF Measure the actual value of resistance R

with an ohmmeter and calculate theoretical value of the time τ = RC.

τ Can be calculated in 3 ways:

1) By direct substitution: τ = CR.

2) 63% of Vm.

3) Using the equation: τ = (t2-t1) / [ln(Yf – Y1) - ln(Yf – Y2)]

Using two measured points.

*Choose any of the three method above to measure τ


Post lab #5

Experiment 5A

INDUCTANCE, CAPACITANCE I-V RELATION AND

TRANSIENTS IN RL AND RC CIRCUITS


Inductor Test: 1-Use DMM to measure the DC resistance RL at 400-mH setting…………

RL = Rs = 50Ω L = 400 mH period of input Vs( t ) (T )=

2-Make an accurate sketch of both signals showing values of time and amplitude. (TP1,TP2)

3-Calculate (L / RL ) 4-Calculate an approximate expression for IL = ( 1/ L) ∫ VL dt Use the 400-mH nominal value of L and VL = Vs( t ). Compared with measure iL (t). Use VL (t) = Vs (t) and di / dl from measurements in the expression VL (t) =L* diL / dt. To calculate an approximation value for L compare with nominal value 400 mH. L / RL =

T / 2 = iL (t)=(1/. 4) * ∫ VL.dt = iL =Vs / Rs=

Capacitor Test: 1-Display the FG output voltage v1 And v2 across Rs together, uses DC coupling on both scope channels.

2- Calculate an approximate expression for iC (t) = C * dv / dt. 3-Use the 0.02 µF Nominal value for C and dvc / dt = dvs / dt . Compared with the measured iC(t).

T/2

ic(t) = C(dvC/dt) = i Measured(t) = Vs/Rs = RL & RC Circuit Transients:

Circuit Transient Tests:-RL 1-Expand the time scale to make an accurate measurement of using the 63% change criterion. 2-Make measurements that will enable you to calculate ( τ ). RC transient Tests: Measure the actual value of resistance R with an ohmmeter and calculate theoretical value of the time τ = RC.

R Measured = ∞ τ = RC =……………………………………………………..


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LAB SHEET 6

Experiment 5B

Transients in RLC circuits

The Under damped Case: 1- Construct the circuit of figure 1 using the following R=1500 ,L=500 mH

C=10 nF

Figure 1

2-Measure the resistance of the inductor used -----------.

3-Display about 2 periods of Oscillation of voltage VR (t) which is proportional to

the desired current i(t). (See Figure 2)

Measure T =

Ip1 = Ip2 =

Note: you need these results to calculate α , ωd, , ω0 using equations (20), (21), (19) respectively then compare these values with theoretical values . The Critically damped Case: 1- Use the same circuit as in figure 1, but Let R: decade Box.

2-Display VR (t) on Oscilloscope, Increase R Gradually until the oscillation just

disappears. Figure (3)

3-Measure the values for:-

Im: Vm/R = tm t1 t2 I12: V/R = 4- Interchange the physical position of Rand C in the test circuit. Display VC (t) on

the oscilloscope and measure its initial value VCO. Note: you need the above results to calculate α using equations ( 25 ), (26) and compare these values with theoretical value obtained using equation (16),also compare the value of Im measured directly with the value calculated using equation (24).

The Over Damped Case:

tm =

t1=

t2 =

Im =

I1 =

I2 =

Note: you need these results to calculate α1, α, and α2 using equations (33),(34),(35) then compare these values with theoretical values .


Post lab #6

Experiment 5B

TRANSIENTS IN RLC CIRCUITS

1. Student Name ……………………………………………………………………… Student ID………………………………………………………………………….. 2. Student Name ……………………………………………………………………… Student ID…………………………………………………………………………..

3. Student Name ……………………………………………………………………… Student ID…………………………………………………………………………..

Transients in RLC circuits:- Under Damped RLC circuit parameters:-

Display VR(t):-

From the measured data, calculate:- 1. α

2. ωo 3. ωd (Compare with theoretical values) Critical damped CASE:

R (decade Box):- ………………………………………………………………………..? -Sketch VR (t), VC (t):

Read a sufficient includes:

1. Im: Vm/R = ………………………………………….. 2. tm:…………………………………………………….. 3. t1……………………………………………………….. 4. t2 ………………………………………………………. 5. I12: V/R =……………………………………………… 6. Im/2: …………………………………………………… Calculate (α), ωo, Im then Compare with theoretical values.

The Over Damped Case: R=25 K ohm’s Display VR (t):

Calculate α1:-……………………………………………………… Calculate α:-……………………………………………………… Calculate α2:- ……………………………………………………… Compare with theoretical values.


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LAB SHEET 7 Experiment 6

SINUSOIDAL AC CIRCUIT MEASUREMENTS

Procedure: Construct the circuit shown in figure 1:- 1-Time difference method:-

Figure 1:- Circuit for Measuring phase Angle between voltage across and currents through RL and RC Impedance

1. Apply the input voltage Vs (t) to oscilloscope CH1. 2. Apply the input voltage V1 (t) which represents the inductor current i1(t) to

CH2. 3. With Vs (t) as a reference, measure the phase angle of V1 (t) using the Time difference method.

Expand the time scale as much as possible to obtain good accuracy in measuring ∆t = t2-t1.

2- Ellipse method:- 1- Place the oscilloscope in X-Y mode to display an ellipse. 2- Measure maximum and intercept values along both axes to determine the phase angle. (See figure 2)

Figure 2:- ellipse method for phase-Angle measurement

Make the ellipse as large as a full screen 3- Apply V2 (t) which represents capacitor current i2 to CH2 and repeat the two measurements. Current and Voltage Phasor Measurements:- 1-Construct the circuit shown in figure 3:-

Figure 3

2-With Vs (t) used as reference, measure the amplitude and phase angle of Vab (t) using the time- difference method. 3- Similarly, measure the amplitude and phase angle of VL(t) and of VC(t), then measure the amplitude and the phase angle of V2(t) and V3(t). Thevenin Equivalent and Maximum Power Transfer Theorem:- Connect the circuit in figure 4

Figure 4

1-Measure the amplitude and phase angle of the open- circuit voltage

Vxy(oc) and the short –circuit current IXY(sc).


Post lab #7

Experiment 6

SINUSOIDAL AC CIRCUIT MEASUREMENTS


1-Time difference method

Method

Time difference method

Θ =

Vs(t) /V1 (t)

Vs(t) /V2(t)

2- Ellipse method

Method

Ellipse method

Θ =

Vs(t) /V1 (t)

Vs(t) /V2(t)

Calculate the average power for the RL and RC circuits using the two equations:

Pavg = (1/2) Vsm Im cos θ Pavg = (1/2) Im2 R Where:- Vsm =amplitude of Vs (t)

θ =Power-factor Angle Im= Vm1/R1, R= R 1 for RL circuit Im= Vm2/R2, R= R2 for RC circuit Compare the two results Current and Voltage Phasor Measurements:- 1-measure Vab (t) using the time- difference method. 3- Similarly, measure the amplitude and phase angle of VL (t) And of VC (t). Thevenin Equivalent and Maximum Power Transfer:- Vxy(oc) IXY(sc) .

From these two measurements find Zth =Rth + jXTh =VXY(OC) /IXY(sc).

• Write a small paragraph to discuss your results then give your Conclusion about all parts of this experiment

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LAB SHEET 8

Experiment 7

SERIES AND PARALLEL RESONANCE

Procedure: Series resonance 1-Construct the RLC circuit shown in the figure below use R=200Ω, L=0.1H, and C=0.1µf.

100 Hz

Vs

VR R

200

Vc

C

0.1uFL1

100 mHRL

Figure 1: RLC CIRCUIT FOR SERIES RESONANCE MEASUREMENTS 2-Connect a 5-Vrms sinusoidal voltage Vs and maintain this value at all frequencies. 3-Display the function generator output voltage Vs (t) on CH1of the scope. 4 -Display the voltage across R (VR (t)) on CH2 of the scope. 5- Begin from f= 100Hz and increase the frequency until a zero phase shift between Vs (t) and VR (t) occurs. This value represents the resonance frequency f0. F0=…………………………………. VR (peak) =………………………. 6- Increase and decrease the frequency required until you get the following values:-

VRmax at

resonance 0.9 VR 0.8 VR 0.7 VR 0.6 VR 0.5 VR 0.4 VR

F1 above resonance

Ф1 above resonance

F2 below resonance

Ф2 below resonance

Parallel resonance:- 1- Construct the circuit of Figure2 with R = 2 K ohm’s L = 80 mH and C = 80 n F.

2- Set Vs to 10-v rms and make sure it is constant during all measurements. 3- With Vs on the Oscilloscope Ch1 And Vp to Ch2 Observe the phase difference between them. 4- While you increase the source frequency from 100 Hz. Resonance is reached when the phase difference becomes exactly zero. **At this point measure the period of the source voltage and the RMS value of:

VP

IL

IC

5- Increase and decrease the frequency required until you get the following values:-

Vpmax at resonance

0.9 Vp 0.8 Vp 0.7 Vp 0.6 Vp 0.5 Vp 0.4 Vp

F1 above resonance

Ф1 above resonance

F2 below resonance

Ф2 below resonance


Postlab 8

Experiment 7

SERIES AND PARALLEL RESONANCE

Procedure: Series resonance

1-After the RLC circuit with R=200Ω, L=0.1H, and C=0.1µf. 2- Display the voltage across R (VR (t)) on CH2 of the scope.

VR (t)

F0=…………………………………. VR (peak) =………………………. *Fill the table below

VRmax at

resonance 0.9 VR 0.8 VR 0.7 VR 0.6 VR 0.5 VR 0.4 VR

F1 above resonance

Ф1 above resonance

F2 below resonance

Ф2 below resonance

From these measurements data Determine:

ωo

α

ω1

ω2

ω3

Qo

ß

ζ

Determine | VL/Vs | ,| VC/Vs |,At resonance and compare with Qo.

Plot | Is| = |VR|/R ,|Zs|=|Vs/Is| And the phase angle of VR VS ω using a

logarithmic scale for ω .

Parallel resonance:-

VP

IL

IC

Vpmax at resonance

0.9 Vp 0.8 Vp 0.7 Vp 0.6 Vp 0.5 Vp 0.4 Vp

F1 above resonance

Ф1 above resonance

F2 below resonance

Ф2 below resonance

From the above measurement data, determine

ωo

α

ω1

ω2

ω3

Qo

ß

ζ

Compare with the theoretical values.

Also, determine |IL/(Vs/R) | ,|IC/(Vs/R) | ,At resonance and compare with Qo

Is Qo is large enough to justify approximate calculations?

---------------------------------------------------------------------------------------------------.

Plot | VP | ,| IP |= | (Vs / R )/ VP | And the phase angle of VP VS ω using a

logarithmic scale for ω.

*Write a small paragraph to discuss your results then give your Conclusion about all parts of this experiment

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