138 Resonance16 Give an expression for the resonant frequency of a parallel circuit
assuming that the resistance in the circuit is very much smaller than the
inductive reactance.
17 Give an expression for the dynamic impedance of a parallel circuit.
18 State what happens to the Q-factor of a parallel circuit as its dynamic
impedance becomes larger.19 State whether the current in a parallel circuit at resonance is a maximum
or a minimum.
20 Give an expression for the bandwidth (B) in terms of the angular resonant
frequency (o J0) and the Q-factor.
6.4 PROBLEMS
1 A coil is connected in series with a capacitor of 20 IxF to a 200 V variable
frequency supply. The current is a maximum at 50 A when the frequency is
set to 50 Hz. Determine the resistance and inductance of the coil.
2 A coil having an inductance of 1 H and a resistance of 5 ~ is connected in
series with a resistance of 5 fl and a capacitor of 15.8 txF. The whole
combination is connected to a 200 V variable frequency supply. Determine
(a) the resonant frequency, (b) the current in the circuit at resonance, (c)
the corresponding voltage developed across the capacitor.
3 A series circuit consists of a 40 ~ resistor, a 0.5 H inductor and a variable
capacitor connected across a 100 V, 50 Hz supply. Calculate (a) the value
of the capacitance required to give resonance, (b) the voltages across the
resistor, the inductor and the capacitor at resonance, and (c) the Q-factor
of the circuit.
4 A bandpass filter consists of a capacitor of 5 nF in series with a coil of
inductance 10 mH having a resistance 5 l~ and a resistor of 75 l-I resistance.
The output voltage is taken across the resistor. Determine (a) the resonant
frequency, (b) the Q-factor of the coil and (c) the bandwidth of the filter.
5 Determine the voltage gain as a ratio (Vo/Vin) and in decibels of the circuit
of Problem 4 at 20 kHz.
6 A voltage Vi is applied to a circuit consisting of a capacitor in series with a
resistor. An output voltage Vo is taken across the resistor (this constitutes
a simple high-pass filter circuit).
(a) Obtain an expression for the voltage gain H(j00).
(b) If 1/CR = 1000 obtain the voltage ratio in dB for oJ = 10; to = 100 and
~o = 1000 rad -1. Comment on the result.
(c) State how the circuit could be converted into a bandpass filter circuit.