3-Phase AC Circuits

Problem 343: A three-phase 230-V circuit serves two single phase loads, A and B. Load A is an induction motor rated 8 hp, 230 V, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the line current on line b.

Problem 344: A four wire 208-V three-phase system is used to supply power to a three-phase 5-hp induction motor and a single phase 6 kW heater connected between line c and the neutral line. The operating efficiency and power factor of the motor are 81 and 71 percent, respectively. Calculate the current in line c. Assume a phase sequence of a-b-c.

Problem 345: A factory is supplied by a three-phase, 3-wire system with the following characteristics: \(V_{ab}=230\angle0^\circ\,V\), \(I_a=110\angle{-36.87^\circ}\,A\); \(V_{bc}=230\angle240^\circ\,V\), \(I_c=125\angle53.13^\circ\,A\). Find line current \(I_b\).

Problem 346: Given a balanced 3-wire, three-phase system serving an unbalanced wye-connected load. Determine the line current in line a. \(V_{ab}=210\angle0^\circ\,V\), \(Z_{an}=10\); \(V_{bc}=210\angle120^\circ\,V\), \(Z_{bn}=10+j10\); \(V_{ca}=210\angle240^\circ\,V\), \(Z_{cn}=10\).

Problem 347: Three resistors 10, 15 and 30 ohmic values are connected in wye-configuration to a balanced 208-volt three-phase supply. Calculate the total power of the system.

Problem 348: Three impedances each 10 + j5 ohms are connected in delta on a balance three-phase source. If the equation of the phase voltage is \(V_{an}=120\sin wt\). What is the equation of the current through the impedance connected across phase A and B?

Problem 349: Two parallel connected loads A and B are supplied by a 440 V, 3-phase, 60 Hz generator. Load A draws an apparent power of 100 kVA at 0.80 pf lagging and load B draws an apparent power of 70 kVA at unity pf. Determine the feeder current.

Problem 350: Two different loads A and B are connected across a balanced 230 V, 3-\(\phi\) lines. Load A is a three-phase load that draws 10 kVA at 70% lagging pf. Load B is a single-phase load connected across lines a and b drawing 5 kVA at unity pf. Determine line current in line a. Assume a phase sequence of a-b-c.

Problem 351: A three-phase motor takes 10 kVA at 0.6 pf lagging from a source of 230 volts. It is in parallel with a balanced delta load having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Determine the total power factor.

Problem 352: A balanced delta load whose impedance is \(45\angle70^\circ\) ohms per branch, a three-phase motor that draws a total of 10 kVA at 0.65 pf lagging and a wye connected load whose impedance is 10 ohms (resistance) per branch are supplied from a three-phase, three-wire, 208 V, 60 Hz feeder. Determine overall power factor of the feeder loads.

Problem 353: A three-phase 230-V circuit serves two single phase loads, A and B. Load A is an induction motor rated 8 hp, 230 V, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the total power factor of the load.

Problem 354: A 440-V three-phase, 3-wire wire, 60 Hz feeder supplies power to two 30-hp induction motors. One motor is operating at full load, 85% efficiency and has a power factor of 90%. The other motor is operating at one-half of its rated horsepower, 89% efficiency and has a power factor of 78%. What is the overall power factor of the system of motors?

Problem 355: Three unequal single-phase loads so connected across the lines of a balanced, 3-phase, 230 volts circuit. The first takes 106 A at 0.78 pf lagging and is connected across lines 1 & 2. The second takes 142 A, at 0.82 pf lagging and is connected across 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging. Determine total apparent power.

Problem 356: Two balanced Y-connected loads A and B are connected across a three-phase 3-wire balanced system. Load A draws 6 kW at 80% power factor lagging while load B draws 12 kW at 83.5% power factor leading. If the current in the three lines are each equal to 8 A, determine the current drawn by load A.

Problem 357: The phase b line voltage and the phase a line current of a balanced three-phase system are V = 220 sin (wt + 210°) and I = 10 sin (wt - 30°), respectively. What is the power of the system.

Problem 358: The following information is given for a delta-connected load of three numerically equal impedances that differ in power factor: Line voltage = 120 volts, \(Z_{ab}=15\angle30^\circ\), \(Z_{bc}=15\angle0^\circ\), \(Z_{ca}=15\angle{-30^\circ}\), phase sequence a-b-c. Calculate the total power drawn by the load.

Problem 359: A three-phase motor takes 10 kVA at 0.6 pf lagging from a source of 230 volts. It is in parallel with a balanced delta load having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Determine the total line current.

Problem 360: In AC circuits, find the total power in kW in an unbalanced three-phase circuit loaded as follows: Phase I = 120 V, 100 A, unity pf. Phase II = 100 V, 230 A, 80% pf and phase III = 110 V, 85 A, 77% pf.

Problem 361: Two single-phase transformers are connected in V (open delta) and serving a delta connected impedance load, each impedance is equal to \(16\angle36.87^\circ\) ohms. If the transformer voltages impressed on the impedances are 240V each (line to line). Solve for the total kVA drawn by the load.

Problem 362: Three impedances, \(Z_{an}=20+j0\), \(Z_{bn}=16+j12\), \(Z_{cn}=5-j15\) ohms, are connected in wye across a 230 V (line to line), 3-phase, 4-wire source. The phase sequence is a-b-c, counterclockwise. Determine the current passing thru the neutral.