6.4 Problems 1397 A circuit consisting of a coil of inductance 250 mH, having a resistance of
20 lq, in parallel with a variable capacitor C is connected to a 200 V 50 Hz
supply. Determine (a) the value of C required for the circuit to resonate,
(b) the power absorbed at resonance, and (c) the ratio of the current
through the capacitor to the supply current at resonance.
8 A resistor of 90 fl resistance is connected in series with a coil of
inductance 500 mH, having a resistance of 10 ~. This series circuit is
connected in parallel with a 20 IxF capacitance across a 250 V variable
frequency supply. Determine (a) the resonant frequency of the circuit, (b)
the resonant frequency if the 90 fl resistor is short circuited and (c) the
current drawn from the supply in each case.
9 A coil of inductance 10 mH and resistance 50 ~ is connected in parallel
with a capacitor of 0.01 ~F. Determine (a) the resonant frequency, (b) the
Q-factor, (c) the bandwidth of the circuit, and (d) the half-power
frequencies.10 A series circuit consisting of an inductance of 0.3 H, having a resistance of
10 1~, and a variable capacitor C~ is supplied from a 100 V, variable
frequency, source.
(a) Determine the value of C1 necessary for the circuit to operate
resonantly at 50 Hz.
(b) A second variable capacitor, C2, is now connected in parallel with the
original circuit and the supply frequency is adjusted to 60 Hz.
Determine the value of C2 in order that the circuit still operates with
minimum current.
11 A coil of resistance 2 11 has a Q-factor of 80 and is to work at a frequency
of 1 kHz. Determine
(a) the value of the equivalent parallel resistance of the coil for the same
Q-factor,
(b) the additional parallel resistance required for the Q-factor to be halved
at the same frequency,
(c) the capacitance required to give the circuit a dynamic impedance of
100 k12, and
(d) the values of the Q-factor and frequency under condition (c).
12 A coil having a Q-factor of 100 is connected in parallel with a capacitor of
100 pF. The circuit resonates at a frequency of 5 MHz. Determine (a) the
bandwidth of the circuit, (b) the amount of resistance required to be
placed in parallel with the capacitor in order to increase the bandwidth to
250 kHz, and (c) the amount of resistance required to be placed in series
with the inductor in order to produce the same bandwidth.
13 The aerial circuit of a radio receiver consists of a tuned circuit comprising
a coil of inductance 100 ~H and resistance 5 ~ in parallel with a variable