Cairo University Prof. Afaf Abdel-Fattah
Faculty of Engineering Circuits(2) ELC 1030 Department of Electronics & Electrical Communications Term (II)
ELECTRIC CIRCUITS
Report (1)
Series Resonance
Cairo University Prof. Afaf Abdel-Fattah
Faculty of Engineering Circuits(2) ELC 1030 Department of Electronics & Electrical Communications Term (II)
Question[1]: Draw the normalized resonance curves for the current in a series resonance circuit having
a quality factor Qs = 20 (for δ = ± 5 % , ± 10 % , ± 20 % & ± 30 %). Plot the phase angle
of the current in the same frequency range and show the effect of increasing Qs.
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Question[2]: In a series resonance circuit L = 65 mH, C = 1.56 nF and R = 5.1 Ω, calculate:
i)The resonance frequency.
ii)The quality factor of the circuit and the bandwidth.
iii)The impedances of the circuit at frequencies 1 % and 10 % above resonance.
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Question[3]: For the circuit shown in figure, calculate the frequency at which series resonance
occurs (the input impedance is real). At what value of the conductance G will it be
impossible to obtain resonance ?
R L
GC
2 Ω 0.1 mH
2 µF0.1
mhoZ
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Question[4]: A generator is connected to a series oscillating circuit has a frequency of 250 KHz. The
oscillating circuit has a constant L = 600 µH, R = 30 Ω and a variable capacitor C.
i)For which value of the capacitor C will the circuit be at resonance ?
ii)For which value of the frequency will the current flowing through the circuit decrease
to one fourth of its value at resonance ?
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Cairo University Prof. Afaf Abdel-Fattah
Faculty of Engineering Circuits(2) ELC 1030 Department of Electronics & Electrical Communications Term (II)
Question[5]: The cutoff frequencies of a series resonance circuit are 5600 and 6000 Hz:
i)Calculate the B.W. of the circuit and Qs .
ii)If the resistance of the circuit is 2 Ω , calculate XL , XC at resonance as well as L and C.
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Question[6]: A series resonance circuit has a resonance frequency of 10 KHz . The resistance of the
circuit is 5 Ω and XC at resonance is 200 Ω , find:
i)The bandwidth and the cutoff frequencies .
ii)Qs of the circuit .
iii)The voltage across the coil and the capacitor at resonance and at a frequency 10 %
below resonance if the input voltage is 300 oV.
iv)The power dissipated in the circuit at resonance and at a frequency 4 % above
resonance.
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Question[7]: Design a series resonance circuit with an input voltage 50 oV to have the following
specifications:
A peak current of 500 mA.
A B.W. of 120 Hz.
A resonance frequency of 8400 Hz.
Calculate the circuit elements and the cutoff frequencies.
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Question[8]: A series resonance circuit of R , L and C is required to be at resonance at a frequency
of 1 MHz. Its Bandwidth is 5 KHz and its input impedance at resonance is 50 Ω .
Calculate R , L and C.
Insert your results in Table 8.
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Cairo University Prof. Afaf Abdel-Fattah
Faculty of Engineering Circuits(2) ELC 1030 Department of Electronics & Electrical Communications Term (II)
Question[9]: Make the necessary derivations to sketch the magnitude of the current I shown in figure
in amperes against frequency in Hertz showing its value at the resonance frequency fs
and the cutoff frequencies f1,2 . Hence , prove that : 21 fffs .
Insert your results in sketch 9.
I 150 Ω
25
Ω
50
mH
30
nF
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Cairo University
Faculty of Engineering
Elec. & Comm. Dept.
Circuits (2)
2019 2020
Report 1 Final Answers
1 Direct substitution 6 B.W. = 250 Hz
f1 = 9875 Hz f2 = 10125 Hz
Qs = 40
VL.res. = 1200|90o VC.res. = 1200|-90
o
VL.10% = 127.0728|173.2429o V
VC.10% = 156.878|-6.7571o V
Pres. = 180 W P4% = 16 W
2 fs = 15.805 kHz
Qs = 1265.68
B.W. = 12.48 Hz
Z = 5.1 + 129.1j Ω
Z = 5.1 + 1232.312j Ω
7 R = 10 Ω
L = 13.2629 mH
C = 0.027 μF
f1 = 8340 Hz f2 = 8460 Hz
3 ωs = 50 kRad/sec
G ≥ (√2) /10 = 0.14142 Ω-1
8 L = 1.59155 mH
C = 15.9155 pF
R = 50 Ω
4 C = 0.67547 nF
f = 265.8846 kHz, 235.664 kHz
9 Proof
5 B.W. = 400 Hz
Q = 14.4914
XL = XC = 28.98275 Ω
L = 0.795774 mH
C = 0.94735 μF