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