Sohag University year 2020/2021
Faculty of Engineering 2nd year elec.
Electrical Engineering department Electrical Circuits (3)
SHEET 2
SERIES RESONANCE
1) In series resonance circuit, R = 0.2 Ω , L=1 mH , C=1 µF. Find:
a) the resonance frequency and the value of Q at resonance.
b) the bandwidth, the frequency between the half power points.
2) A 53 Ω resistor is in series with an inductor. The coil has an inductance of 100 µH & a
parallel resistance of 56.5 Ω.
a) Reduce the circuit to its equivalent series circuit and find QL &Q at 1 Mhz.
b) Verify your results for Q by using the basic definition of stored and dissipated energy.
3) It is required that a series circuit R,L,C be resonant at 1 Mhz. Its bandwidth is to be 5 kHz
and its input impedance is to be 50 Ω.Find R,L and C.
4) It is required that a series circuit of R,L,C be resonant at 1.5 Mhz, its band width is to be 5
kHz .Find R,L if C =10 pF.
5) In a series resonance circuit , R=5.1 Ω , L=65 µH ,C=1.56 nF. Find
A) Resonant frequency
b) The quality factor Q
c) The impedance of the circuit at a frequency 1% above resonance .
6) If Q0δ = m2 in the circuit of problwm 5 .Compute the admittance its real and imaginary
parts:
a)Without introducing any assumption of simplification
b) Using the assumption that leads to the universal resonance curve.
c)Is the error discovered significat (i.e. greater than 1%)
7) Show that in aseries R,L,C circuit , the value of Q0 can be defined as the ratio of the rms
value of the voltage across the capacitor to the rms value of the voltage source at resonace.
If the terminals of the combination are a‐b :
a) Plot to scale a curve of Yab as a function of frequency for R=40 Ω,L= 1 mH ,C=0.1 µF.
b) Plot to scale the angle of Yab as a function of frequency
c)From part (a), indicate on the curve the resonance frequency, the half power points and
determine the bandwidth.
8) The admittance of a series RLC circuit is maximum at a frequency of 5 kHz and 50% of its
maximum at 4 kHz.
a) At which other frequency the admittance is 50% of its maximum
b) Calculate the upper and lower half power frequencies
c)Calculate Q0
9) The lower and upper half power frequencies of a series RLC circuit are 5& 20 kHz
respectively.
a) Find Q
b) Calculate the frequencies at which the angle of the complex admittance is ±100.
10) A series resonant circuit consists of a coil has an inductance of 0.1 mH and a Q of 200 at
the resonant frequency, in series with a capacitor of 100 µF.
A constant voltage source of 10 V is applied to the circuit. Determine:
a) The resonant frequency in rad/sec
b) The coil resistance
c) C) The bandwidth and the cut‐off frequencies
d) The power dissipated at the cut‐off frequencies
11) A 30 ohm resistance is connected in series with a choke (pure inductance) across a 110 V,
50 Hz supply. Calculate the inductance of the choke if the resistance dissipates 250 Watts.
Calculate also the capacitance of condenser, which when connected across the combination,
raises the supply power factor to unity. Draw a vector diagram (not necessarily to scale).
12) A series resonant circuit has a resonant frequency of 10 kHz. If the resistance of the circuit
is 5 ohm and Xc at resonance is 200 ohm, Find the bandwidth ,the cut‐off frequencies ,the Q of
the circuit. If the input voltage is 30 Find the voltages across the coil and capacitor. Compute
the power dissipated in the circuit at resonance.
Best regards,
Dr. Ahmed Refai
Eng. Abdel Hady Ramadan
