EENG20005 - Electrical Energy Conversion and Supply
Example Sheet 4 – Power Theory
1. A sinusoidal current source supplies 2A at a frequency of 100Hz into a series circuit consisting of a 35Ω resistor and a 0.03H inductor. Calculate the circuit impedance in both polar and rectangular forms, and find the voltage developed across the resistor and inductor combination. (Take the current as the reference phasor.)
2. Sketch a phasor diagram for Question 1. Again, use the current as the reference phasor and show the supply voltage and the voltages across the resistor and the inductor.
3. For the circuit in Question 1, find the apparent, real and reactive powers supplied.
4. A circuit consists of a 200Ω resistor in series with a parallel combination of a 1H inductor and a 4μF capacitor and is supplied by a 240V, 50Hz source. Find the circuit impedance, current, real power drawn and reactive power drawn.
5. A circuit consists of a 100Ω resistor in series with a parallel combination of a 150Ω resistor and 1H inductor. The circuit is supplied from a 240V, 50Hz supply. Calculate the impedance of the circuit and give the answer in Cartesian and polar forms. Find the magnitude of the current in each of the three circuit elements and the real power and VAr drawn from the supply.
6. An AC motor operating from a 50Hz supply can be represented by a 200Ω resistor in series with a 1H inductor. Find the power factor for the motor and the value of the parallel capacitor that will increase the power factor to 0.9.
7. Measurements on a 240V AC motor reveal that its power consumption is 12kW and the supply current is 60A. Find the power factor, the reactive VAr and the impedance of the motor making the assumption that the motor is inductive.
8. The current drawn by a 230V 60Hz electrical appliance is measured at 7A and is found to lag behind the applied voltage by 24°. What value of capacitance should be placed in parallel with the load to correct the power factor to one?