1 )A coil of resistance 20 and inductance 100 mH is connected in parallel with a 50 F capacitor across a 30 V variable-frequency supply. Determine (a) the resonant frequency of the circuit, (b) the dynamic resistance, (c) the current at resonance, and (d) the circuit Q-factor at resonance. [(a) 63.66 Hz (b) 100 (c) 0.30 A (d) 2] 2 A 25 V, 2.5 kHz supply is connected to a network comprising a variable capacitor in parallel with a coil of resistance 250 and inductance 80 mH. Determine for the condition when the supply

current is a minimum (a) the capacitance of the capacitor, (b) the dynamic resistance, (c) the supply current, (d) the Q-factor, (e) the bandwidth, (f) the upper and lower half-power frequencies and (g) the value of the circuit impedance at the 3 dB frequencies

2)3 A 0.1 F capacitor and a pure inductance of 0.02 H are connected in parallel across a 12 V variable-frequency supply. Determine (a) the resonant frequency of the circuit, and (b) the current circulating in the capacitance and inductance at resonance. [(a) 3.56 kHz (b) 26.84 mA] 4 A coil of resistance 300 and inductance 100 mH and a 4000 pF capacitor are connected (i) in series and (ii) in parallel. Find for each connection (a) the resonant frequency, (b) the Q-factor, and (c) the impedance at resonance.

3)A network comprises a coil of resistance 100 and inductance 0.8 H and a capacitor having capacitance 30 F. Determine the resonant frequency of the network when the capacitor is connected (a) in series with, and (b) in parallel with the coil. Figure 29.11 [(a) 32.5 Hz (b) 25.7 Hz] 6 Determine the value of capacitor C shown in Figure 29.10 for which the resonant frequency of the network is 1 kHz. [2.30 F] 7 In the parallel network shown in Figure 29.11, inductance L is 40 mH and capacitance C is 5 F. Determine the resonant frequency of the circuit if (a) RL D 0 and (b) RL D 40 . [(a) 355.9 Hz (b) 318.3 Hz] 8 A capacitor of reactance 5 is connected in series with a 10 resistor. The whole circuit is then connected in parallel with a coil of inductive reactance 20 and a variable resistor. Determine the value of this resistance for which the parallel network is resonant

4)Determine, for the parallel network shown in Figure 29.12, the values of inductance L for which the circuit is resonant at a frequency of 600 Hz. [2.50 mH or 0.45 mH] 10 Find the resonant frequency of the two-branch parallel network shown in Figure 29.13. [667 Hz] 11 Determine the value of the variable resistance R in Figure 29.14 for which the parallel network is resonant. [11.87 ] 12 For the parallel network shown in Figure 29.15, determine the resonant frequency. Find also the value of resistance to be connected in series with the 10 F capacitor to change the resonant frequency to 1 kHz. [928 Hz; 5.27 ] Parallel resonance and Q-factor 529 Figure 29.13 Figure 29.14 Figure 29.15 13 Determine the overall Q-factor of a parallel arrangement consisting of a capacitor having a Q-factor of 410 and an inductor having a Q-factor of 90. [73.8] 14 The value of capacitance in an LR-C parallel network is 49.74 nF. If the resonant frequency of the circuit is 200 kHz and the bandwidth is 800 Hz, determine for the network (a) the Q-factor, (b) the dynamic resistance, and (c) the magnitude of the impedance when the supply frequency is 0.5% smaller than the tuned frequency.

5)In a Schering bridge network PQRS, the arms are made up as follows: PQ a standard capacitor C1, QR a capacitor C2 in parallel with a resistor R2, RS a resistor R3, SP the capacitor under test, represented by a capacitor Cx in series with a resistor Rx. The detector is connected between Q and S and the a.c. supply is connected between P and R. (a) Sketch the bridge and derive the equations for Rx and Cx when the bridge is balanced. (b) Evaluate Rx and Cx if, at balance C1 D 5 nF, R2 D 300 , C2 D 30 nF and R3 D 1.5 k

6)A coil of inductance 25 mH and resistance 5 is connected in series with a variable capacitor C. If the supply frequency is 1 kHz and the current flowing is 2 A, determine, for series resonance, (a) the value of capacitance C, (b) the supply p.d., and (c) the p.d. across the capacitor. (8) 3 An L-R-C series circuit has a peak current of 5 mA flowing in it when the frequency of the 200 mV supply is 5 kHz. The Q-factor of the circuit under these conditions is 75. Determine (a) the voltage across the capacitor, and (b) the values of the circuit resistance, inductance and capacitance.

7)A coil of resistance 15 and inductance 150 mH is connected in parallel with a 4 F capacitor across a 50 V variable-frequency supply. Determine (a) the resonant frequency of the circuit, (b) the dynamic resistance (c) the current at resonance, and (d) the circuit Q-factor at resonance. (10) C 5 2 mH Figure A9.1 5 For the parallel network shown in Figure A9.1, determine the value of C for which the resonant frequency is 2 kHz.

8)Label branch currents and their directions on the circuit diagram. The directions chosen are arbitrary but, as a starting-point, a useful guide is to assume that current flows from the positive terminals of the voltage sources. This is shown in Figure 30.2 where the three branch currents are expressed in terms of I1 and I2 only, since the current through resistance R, by Kirchhoff's current law, is (I1 C I2) Figure 30.1 (ii) Divide the circuit into loops two in this ease (see Figure 30.2) and then apply Kirchhoff's voltage law to each loop in turn. From loop ABEF, and moving in a clockwise direction (the choice of loop direction is arbitrary), E1 D I1r C I1 C I2R (note that the two voltage drops are positive since the loop direction is the same as the current directions involved in the volt drops). Use Kirchhoff's laws to find the current flowing in each branch of the network.

9)1 For the network shown in Figure 30.11, determine the current flowing in each branch. [50 V source discharges at 2.08 A, 20 V source charges at 0.62 A, current through 20 resistor is 1.46 A] 2. Determine the value of currents IA, IB and IC for the network shown in Figure 30.12. [IA D 5.38 A, IB D 4.81 A, IC D 0.58 A] 3. For the bridge shown in Figure 30.13, determine the current flowing in (a) the 5 resistance, (b) the 22 resistance, and (c) the 2 resistance. [(a) 4 A (b ) 1 A (c) 7 A] 4. For the circuit shown in Figure 30.14, determine (a) the current flowing in the 10 V source, (b) the p.d. across the 6 resistance, and (c) the active power dissipated in the 4 resistance

10)Use Kirchhoff's laws to determine the current flowing in each branch of the network shown in Figure 30.15. [406 90 V source discharges at 4.406 74.48 A 206 0 V source discharges at 2.946 53.13 A current in 10 resistance is 1.976 107.35 A (downward)] Figure 30.15 6. For the network shown in Figure 30.16, use Kirchhoff's laws to determine the current flowing in the capacitive branch. [1.58 A] 7. Use Kirchhoff's laws to determine, for the network shown in Figure 30.17, the current flowing in (a) the 20 resistance, and (b) the 4 resistance. Determine also (c) the p.d. across the 8 resistance, and (d) the active power dissipated in the 10 resistance