TUTORIAL QUESTIONS
1. A 0.15microF capacitor and a pure inductance of 0.01 H are connected in parallel across
a 10 V, variable frequency supply. Determine (a) the resonant frequency of the circuit,
and (b) the current circulating in the capacitor and inductance
2. A current of (15 + j8) A flows in a circuit whose supply voltage is (120 + j200) V.
Determine the active power and reactive power
3. A 30microF capacitor is connected in parallel with a coil of inductance50 mH and
unknown resistance R across a 120 V, 50 Hz supply. If the circuit has an overall power
factor of 1 find (a) the value of R, (b) the current in the coil, and (c) the supply current.
4. A coil of resistance 25ohms and inductance 150 mH is connected in parallel with a
10microF capacitor across a 60 V, variable frequency supply. Calculate (a) the resonant
frequency, (b) the dynamic resistance, (c) the current at resonance and (d) the Q-factor at
resonance.
5. A coil of inductance 80 mH and negligible resistance is connected in series with a
capacitance of 0.25 µF and a resistor of resistance 12.5 Ω across a 100 V, variable
frequency supply. Determine
(i) The resonant frequency ii. The current at resonance.
(ii) How many times greater than the supply voltage is the voltage across the reactance at
resonance
6. A coil of resistance 1.5 kiloohms and 0.25 H inductance is connected in parallel with a
variable capacitance across a 10 V, 8 kHz supply. Calculate (a) the capacitance of the
capacitor when the supply current is a minimum, (b) the dynamic resistance, and (c) the
supply current.
7. A 1500 nF capacitor is connected in parallel with a 16 _ resistor across a 10 V, 10 kHz
supply. Calculate (a) the current in each branch, (b) the supply current, (c) the circuit
phase angle, (d) the circuit impedance, (e) the power consumed, (f) the apparent power,
and (g) the circuit power factor. Draw the phasor diagram.
8. A capacitor C is connected in parallel with a resistance R across a 60 V, 100 Hz supply.
The supply current is 0.6 A at a power factor of 0.8 leading. Calculate the value of R and
C.
9. A 415 V alternator is supplying a load of 55 kW at a power factor of 0.65 lagging.
Calculate (a) the kVA loading and (b) the current taken from the alternator. (c) If the
power factor is now raised to unity find the new kVA loading.
10. A motor takes a current of 10 A when supplied from a 250 V a.c. supply. Assuming a
power factor of 0.75 lagging find the power consumed. Find also the cost of running the
motor for 1 week continuously if 1 kWh of electricity costs 7.20 p.
11. Find the resonant frequency of a series a.c. circuit consisting of a coil of resistance
10ohms and inductance 50 mH and capacitance 0.05 μF. Find also the current flowing at
resonance if the supply voltage is 100 V.
12. The current at resonance in a series L–C–R circuit is 0.2 mA. If the applied voltage is 250
mV at a frequency of 100 kHz and the circuit capacitance is 0.04 μF, find the circuit
resistance and inductance.
13. A coil of resistance 25ohms and inductance 100 mH is connected in series with a
capacitance of 0.12 μF across a 200 V, variable frequency supply. Calculate (a) the
resonant frequency, (b) the current at resonance and (c) the factor by which the voltage
across the reactance is greater than the supply voltage.
14. A 40 μF capacitor in series with a coil of resistance 8 ohms and inductance 80 mH is
connected to a 200 V, 100 Hz supply. Calculate (a) the circuit impedance, (b) the current
flowing, (c) the phase angle between voltage and current, (d) the voltage across the coil,
and (e) the voltage across the capacitor.
15. The resistance of a 2 m length of cable is 2.5 ohms. Determine (a) the resistance of a 7 m
length of the same cable and (b) the length of the same wire when the resistance is 6.25
ohms.
16. Some aluminium wire has a resistance of 50 ohms at 20°C. The wire is heated to a
temperature of 100°C. Determine the resistance of the wire at 100°C, assuming that the
temperature coefficient of resistance at 0°C is 0.004/°C
17. A d.c. source has an open-circuit voltage of 20 V and an internal resistance of 2 ohms .
Determine the value of the load resistance that gives maximum power dissipation. Find
the value of this power
18. A star-connected load consists of three identical coils, each of inductance 159.2 mH and
resistance 50 ohms. If the supply frequency is 50 Hz and the line current is 3 A determine
(a) the phase voltage and (b) the line voltage
19. Three inductive loads, each of resistance 4 ohms and reactance 9 are connected in delta.
When connected to a 3-phase supply the loads consume 1.2 kW. Calculate (a) the power
factor of the load, (b) the phase current, (c) the line current and (d) the supply voltage.