EE 202 Electric Circuits Theory 2

Electric Circuits Theory 2Lesson 4Power Factor and Parallel AC CircuitsPrepared by:Engr. Michael M. Salvahan, ECE, ECTPower Triangle and Power FactorLesson 4: Power Factor and Parallel AC CircuitsApparent Power the product of the current and voltage of the circuit.

Real Power the capacity of the circuit for performing work in a particular time.

Reactive Power power that continuously bounce back and forth between source and load.

Power Factor defined as the ratio of the real power flowing to the load, to the apparent power in the circuit and is a dimensionless number in the closed interval of -1 to 1.

Power Triangle and Power FactorLesson 4: Power Factor and Parallel AC Circuits

Power Triangle and Power FactorLesson 4: Power Factor and Parallel AC CircuitsSample Problems:A pure inductance is connected to a 150 V, 50 Hz supply, and the apparent power of the circuit is 300 VA. Find the value of the inductance.A transformer has a rated output of 200 kVA at a power factor of 0.8. Determine the rated power output and the corresponding reactive power.Answer: L = 0.239 HAnswer: P = 160 kW, Q = 120 kVARPower Triangle and Power FactorLesson 4: Power Factor and Parallel AC CircuitsSample Problems:The power taken by an inductive circuit when connected to a 120 V, 50 Hz supply is 400 W and the current is 8 A. Calculate (a) the resistance, (b) the impedance, (c) the reactance, (d) the power factor, and (e) the phase angle between voltage and current.A circuit consisting of a resistor in series with a capacitor takes 100 watts at a power factor of 0.5 from a 100 V, 60 Hz supply. Find (a) the current flowing, (b) the phase angle, (c) the resistance, (d) the impedance, and (e) the capacitance.Ans: R = 6.25 , Z = 15 , XL = 13.64 , P.F. = 0.4167, = 6522 laggingAns: I = 2 A, = 60 leading, R = 25 , Z = 50 , XC = 61. 26 FParallel AC CircuitsLesson 4: Power Factor and Parallel AC CircuitsIn parallel circuits, the voltage is common to each branch of the network and is thus taken as the reference phasor when drawing phasor diagrams.RL Parallel CircuitRC Parallel CircuitLC Parallel CircuitRL-C Parallel CircuitRL Parallel AC CircuitLesson 4: Power Factor and Parallel AC CircuitsSample Problem:A 20 resistor is connected in parallel with an inductance of 2.387 mH across a 60 V, 1 kHz supply. Calculate (a) the current in each branch, (b) the supply current, (c) the circuit phase angle, (d) the circuit impedance, and (e) the power consumed.Answer:IR = 3 A, IL = 4 A, I = 5 A, = 538 lagging, Z = 12 , P = 180 W RC Parallel AC CircuitLesson 4: Power Factor and Parallel AC CircuitsSample Problem:A 30 F capacitor is connected in parallel with an 80 resistor across a 240 V, 50 Hz supply. Calculate (a) the current in each branch, (b) the supply current, (c) the circuit phase angle, (d) the circuit impedance, (e) the power dissipated, and (f) the apparent power.Answer:IR = 3 A, IC = 2.262 A, I = 3.757 A, = 371 leading, Z = 63.88 , P = 720 W, S = 901.7 VA RC Parallel AC CircuitLesson 4: Power Factor and Parallel AC CircuitsSample Problem:A capacitor C is connected in parallel with a resistor R across a 120 V, 200 Hz supply. The supply current is 2 A at a power factor of 0.6 leading. Determine the values of C and R.Answer:R = 100 , C = 10.61 F LC Parallel AC CircuitLesson 4: Power Factor and Parallel AC CircuitsSample Problem:A pure inductance of 120 mH is connected in parallel with a 25 F capacitor and the network is connected to a 100 V, 50 Hz supply. Determine (a) the branch currents, (b) the supply current and its phase angle, (c) the circuit impedance, and (d) the power consumed.Answer:IL = 2.653 A, IC = 0.786 A, I = 1.867 A, Z = 53.56 , P = 0 W RL-C Parallel AC CircuitLesson 4: Power Factor and Parallel AC CircuitsSample Problem:A coil of inductance 159.2 mH and resistance 40 is connected in parallel with a 30 F capacitor across a 240 V, 50 Hz supply. Calculate (a) the current in the coil and its phase angle, (b) the current in the capacitor and its phase angle, (c) the supply current and its phase angle,(d) the circuit impedance, (e) the power consumed, (f) the apparent power, and (g) the reactive power.Answer:ILR = 3.748 A, LR = 5120 lagging,IC = 2.262 A, C = 90 leading, I = 2.434 A, = 1550 lagging Z = 98.60 , P = 562 W, S = 584.2 VA, Q = 159.4 VAR Things turn out best for the people who make the best of the way things turn out.