GAZI UNIVERSITY
FACULTY OF ENGINEERING AND ARCHITECTURE
DEPARTMENT OF
ELECTRICAL AND ELECTRONICS ENGINEERING
EM 222
CIRCUIT ANALYSIS II
LABORATORY MANUAL
2008-2009 SPRİNG
GAZI UNIVERSITY
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
EM222 CIRCUIT ANALYSIS II LABORATORY
EXPERIMENT # 1
I. THE EFFECT OF FREQUENCY ON XC
Purpose:
To investigate the reactance of a capacitor, and to see how the capacitor reactance is chanced with series and parallel combinations of capacitors.
Theory:
The impedance is defined by Z = V / I, V and I are rms values. The impedance is purely resistive, if applied voltage (or current) is ac signal, and if the load is a resistor. In the case, the reactance is being zero. Impedance of a capacitor is purely reactive, having zero resistive components. The capacitive reactance is denoted by XC = -1 / WC and has a resistance dimension ohm.
Figure 1.1. Connection diagram
Experimental Work:
A. Construct the RC circuit which is given in figure 1.1
1. Connect the signal generator to the input of the circuit, and keep the input signal voltage constant.
2. Measure the output voltage when the input voltage is 10 VPP and frequency is f = 1 kHz.
3. Repeat the measurement for the same frequency but different capacitors.
4. Fill in the table 1.1 according to your measurements and calculations.
5. Calculate IC = [(VS2 - VC2)1/2] / R rms, Xc1 = VC/ IC and XC2 = 1 / WC for all. of your measurements (notice that the measurements values are vectorial)
6. Plot the XC1 and XC2 againts C (show in the same graph).
7. Repeat the measurements for constant capacitors and different frequencies.
8. Fill in the table1.2 according to your measurements and calculations.
9. Plot XC1 and XC2 against f.
Table 1.1
F(Hz) / VS(pp) / V0(pp) / IC rms / XC1 / XC2 / C(F)1 kHz / 1 uF
1 kHz / 2.2 uF
1 kHz / 3.3 uF
Table 1.2
F(Hz) / VS(pp) / V0(pp) / IC rms / XC1 / XC2 / C(F)500 Hz / 1 uF
1000 Hz / 1 uF
2000 Hz / 1 uF
3000 Hz / 1 uF
5000 Hz / 1 uF
B. Use two unknown capacitors in figure 1.1
1. Connect two unknown capacitors in series with a source, and adjust the signal generator to VS=10 Vpp, f = 1 kHz.
2. Measure V0 (pp) and find total capacitance.
3. Connect the same capacitors in parallel across the source and adjust signal generator to 10 Vpp, f =1 kHz and repeat part B.2
Results and Conclusions:
1. By using table 1.1 and table 1.2
a) Compare XC1 and XC2
b) How does C affect XC1 and XC2?
c) How does ‘ f ’ affect XC1 and XC2?
2. Compare parallel and series recombination.
II. THE EFFECT OF FREQUENCY ON XL
Purpose:
To investigate the reactance of inductor, and to see how the inductor reactance is chanced with series and parallel combinations of inductors .
Theory:
The impedance is defined by Z = V / I, V and I are rms values.
The impedance is purely resistive, if the applied voltage (or current) is ac signal, and if the load is a resistor. In the case the reactance is being zero. Impedance of an inductor is purely reactive, having zero resistive components. The inductance reactance is denoted by XL = WL and has a resistance dimension ohm.
Figure 1.2 Connection diagram.
Experimental Work:
A. Construct the RL circuit, which is given in figure 1.2.
1. Connect the signal generator to the input of the circuit, and keep constant the input signal voltage.
2. Measure the output voltage when the input voltage is 10 Vpp and frequency is f = 1 kHz.
3. Repeat the measurement for the same frequency but different capacitors.
4. Fill in the 1.3 according to your measurements and calculations.
5. Calculate IL = [( Vs2 - VL2 )1/2 ] / R rms, XL1 = VC / IL and XL2 = WL for all of your measurements (notice that the measurement values vectorial).
6. Plot the XL1 and XL2 against L (show in the same graph).
7. Repeat the measurements for constant inductance and different frequencies.
8. Fill in the table 1.4 according to your measurements and calculations.
Table 1.3
f (Hz) / VS (pp) / Vo (pp) / IL rms / XL 1 / XL 1 / L1 kHz / 470 uH
1 kHz / 1.5 mH
1 kHz / 10 mH
Table 1.4
f (Hz) / VS (pp) / Vo (pp) / IL rms / XL 1 / XL 1 / L500 Hz / 10 mH
1000 Hz / 10 mH
2000 Hz / 10 mH
3000 Hz / 10 mH
5000 Hz / 10 mH
B. Use two unknown inductors in figure 1.2.
1. Connect two unknown inductors in series with a source, VS = 5 Vpp, f = 1 kHz.
2. Measure V0 (pp) and find total inductance.
3. Connect the same inductors in parallel across the source, 5 Vpp, f = 1 kHz and repeat part B.1.
Results and Conclusions:
1. By using table 1 .3 and table 1.4.
a) Compare XL1 and XL2.
b) How does L affect XL1 and XL2?
c) How does f affect XL1 and XL2?
Equipment and Components
Oscilloscope (dual trace)
Signal Generator (0-200kHz)
Protoboard
Resistors
Capacitors
Inductors
GAZI UNIVERSITY
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
EM222 CIRCUIT ANALYSIS II LABORATORY
EXPERIMENT # 2
I . SERIES RC CIRCUIT
Purpose:
To investigate relationship between current and voltage in series RC circuit.
Theory:
A series RC circuit consists of a resistor and a capacitor, which is connected in series to an ac source (figure 2.1.a). When an ac voltage is applied to a resistor R, the current I passing through the resistor is in the same phase with the applied voltage but if an ac voltage is applied to a capacitor C, current leads the voltage by 90o. This is shown in figure 2.1.b as vector diagram.
Figure 2.1. (a) RC circuit Figure 2.1. (b)Vector diagram
In such a RC circuit, The angle between voltage drop VR at the resistor and the current passing through the resistor is zero as shown in figure 2.1.b . However voltage drop Vc at the capacitor lags I and VR by 90o. Summation of Vc and VR gives Vs (figure 2.1.b). “The angle q” . In series RC circuit total impedance is;
ZT = (R2 + Xc2)1/2 , q = tan –1 Xc / R
Experimental Work:
A. To find phase angle q by using vector diagram
1. Construct the circuit which is given in figure 2.1.a.
2. Set the signal generator to the input of the circuit, and adjust 4Vpp and f = 1kHz
3. Measure Vc and compute VR, Ic, Xc
4. Draw vector diagram of the circuit by using your measurements and calculations. Then, find phase angle q
5. Find phase angle q from Lissajous pattern.
6. Calculate and record q¢ from the equation q¢ = tan-1 Xc / R
B. To investigate VR, Vc, Ic, Xc and q according to the frequency
1. Keep the signal generator voltage constant and vary the frequency of the generator.
2. Measure Vc and compute VR, Ic, Xc and fill in the table 2.1.
3. Repeat steps A-5 A-6 for different frequencies
Table3.1
F(Hz) / VC(pp) / VR(pp) / IC(rms) / XC / q / q’Results and conclusions:
1. By using your measurements and calculations;
a) Compare q and q¢ from step B-3
b) Evaluate how f effects q.
c) Plot the q against f
II . SERIES RL CIRCUIT
Purpose:
To investigation relationship between current and voltage in series RL circuit.
Theory:
A series RL circuit consists of a resistor and an inductor connected in series to an ac voltage source (figure 2.2.a). When an ac voltage is applied to a resistor R, The current I passing through the resistor is in the same phase with the applied voltage but if an ac voltage is applied to an inductor L, current lags the voltage by 90o. This is shown in figure 2.2.b as vector diagram.
Figure 2.2. (a) RL circuit (b) Vector diagram
In such a RL circuit, the angle between voltage drop VR at the resistor and the current passing through the resistor is zero as shown in figure 2.2.b. Also voltage drop VL at the inductor leads I and VR gives VS (figure 2.2.b). The angle between VS and I is called “Phase angle q”. In series RL circuit total impedance is;
Z = (R2 + XL2) ½ q = tan-1 XL / R
Experimental Work:
A. To find phase angle q by using vector diagram
1. Construct the circuit which is given in figure2.2.a
2. Set the signal generator to the input of the circuit, and adjust 4Vpp and f = 1 kHz
3. Measure VL and compute VR, IL, XL
4. Draw vector diagram of the circuit by using your measurements and calculations. Then, find phase angel q.
5. Find phase angel q from Lissajous pattern.
6. Calculate and record q¢ from the equation q¢ = tan-1 XL / R
B. To investigate VR, VL, IL, XL and q according to the frequency.
1. Keep the signal generator voltage constant and vary the frequency of the generator.
2. Measure VL and compute VR, VL, IL, XL and fill in the table 2.2
3. Repeat steps A-5 and A-6 for different frequencies.
Table 2.2
F(Hz) / VS(pp) / V0(pp) / IL(rms) / XL1 / XL2 / L(H)Results and conclusions:
1. By using yours measurements and calculations:
a) Compare q and q¢ from step B-3
b) Evaluate how f effects q.
c) Plot q against f.
Equipment and Components
Oscilloscope (dual trace)
Signal Generator (0-200kHz)
Protoboard
Resistors
Capacitors
Inductors
GAZI UNIVERSITY
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
EM222 CIRCUIT ANALYSIS II LABORATORY
EXPERIMENT # 3
I. PARALLEL RC CIRCUIT
Purpose:
To investigate properties of parallel RC circuit.
Theory:
In a parallel RC circuit, a resistor and a capacitor are connected in parallel to a current source and each other as shown in Figure 3.1.a. In the circuit, it is chosen the assignments given by IR, IC and Vo. The vector diagram of parallel RC circuit is shown in Figure 3.1.b.
Figure 3.1.a. RC circuit Figure 3.1.b. Vector diagram
The current of the source I is divided between R and C, and the phase angle q is between VS (or IR) and I is as shown in the equation below.
I=IR+IC
According to vector diagram;
I=(IR2+IC2)1/2 q=arctan|IC|/|IR|
The equivalent impedance of two elements connected in parallel is equal to;
Z=R*XC/(R+XC)
Figure 3.2 Connection diagram
Experimental Work:
A. To find phase angle q by using vector diagram
1. Construct the circuit which is given in Figure 3.2.
2. Set the signal generator to the input of the circuit and adjust 4 Vpp, at f=1kHz.
3. Measure V1, V2 and compute I1 and I2.
4. Draw vector diagram of the circuit by using your measurement and calculations. Then find phase angle q
5. Find phase angle q from Lissajous pattern.
6. Calculate and record q’ from the equation below.
q’=arctan|I1|/|I2|
B. To investigate V1, V2, I1, I2 and q according to the frequency.
1. Keep constant the signal generator voltage and vary the frequency of the generator.
2. Measure V1 and V2 and compute I1, I2 and fill the table 3.1.
3. Repeat steps A-5 and A-6 for different frequencies.
Table 3.1.
F (Hz) / V1(pp) / V2(pp) / I1 / I2 / q / q’Results and Conclusions:
By using your measurements and calculations;
1. Compare q and q’ from step B-3,
2. Evaluate how f effects q,
3. Plot the q against f.
II. PARALLEL RL CIRCUIT
Purpose:
To investigate properties of parallel RL circuit.
Theory:
In a parallel RL circuit, a resistor and an inductor are connected in parallel to a current source and each other as shown in Figure 3.3.a. In the circuit, it is chosen the assignments given by IR, IC and Vo.
The vector diagram of parallel RL circuit is shown in Figure 3.3.b.
Figure 3.3.a. RL circuit Figure 3.3.b. Vector diagram
The current of the source I is divided between R and L, and the phase angle q is between VS (or IR) and I is as shown in the equation below.
I=IR+IL
According to vector diagram;
I=(IR2+IL2)1/2 q=arctan|IL|/|IR|
The equivalent impedance of two elements connected in parallel is equal to;
Z=R*XL/(R+XL)
Figure 3.4 Connection diagram
Experimental Work:
A. To find phase angle q by using vector diagram
1. Construct the circuit which is given in Figure 3.4.
2. Set the signal generator to the input of the circuit and adjust 4 Vpp, at f=1kHz.
3. Measure V1, V2 and compute I1 and I2.
4. Draw vector diagram of the circuit by using your measurement and calculations. Then find phase angle q.
5. Find phase angle q from Lissajous pattern.
6. Calculate and record q’ from the equation below.
q’=arctan|I1|/|I2|
B. To investigate V1, V2, I1, I2 and q according to the frequency.
1. Keep constant the signal generator voltage and vary the frequency of the generator.
2. Measure V1 and V2 and compute I1, I2 and fill the table 3.2.
3. Repeat steps A-5 and A-6 for different frequencies.
Table 3.2.
F (Hz) / V1(pp) / V2(pp) / I1 / I2 / q / q’Results and Conclusions:
By using your measurements and calculations;
1. Compare q and q’ from step B-3,
2. Evaluate how f effects q,
3.Plot the q against f.
Equipment and Components
Oscilloscope (dual trace)