3-Phase AC Circuits

Problem 323: A 170 kV, 3-phase electric source delivers 200 MVA to a balanced load, which has a power factor of 90% lagging. What is the line current?

Problem 324: A three-phase motor is rated 50 hp, 440 volts and 85% power factor. What is its rated current?

Problem 325: A balanced 3-phase load draws 120 amperes line current at 230 volts line to line, 0.848 pf lagging current. Solve for the real power.

Problem 326: A generator supplies three-phase power to balanced load. The voltage is 230 volts, the current is 18 A and the power factor is 85%. What is the power?

Problem 327: A balanced 3-phase load draws 75 amperes line current at 230 V line to line and 0.848 lagging power factor. Solve for the reactive power being drawn.

Problem 328: The input power factor to a three-phase, 6-poles, 460 volts, 60 Hz, 50-hp induction motor is 0.62 as 20 A is drawn by the motor. Find the power input to the motor.

Problem 329: A 460 volt, three-phase motor draws 208 A with a power factor of 0.91 lagging. Calculate the kW input to the motor.

Problem 330: Determine the ratio of the line current drawn by three identical impedances connected in wye to the line current drawn by the same impedances connected in delta. Both connections being impressed with the same balanced 3-\(\phi\) voltages.

Problem 331: A wye-connected load has a \(5\angle20^\circ\) ohm impedance per phase and is connected across a 120-V three-phase source. Calculate the line current.

Problem 332: A balanced delta connected load having impedance per phase of \(20\angle36.87^\circ\) ohms is supplied from a balanced 3-phase, 240 V source. Determine the total real power.

Problem 333: Three condensers, each having a capacity of 75 microfarads are connected in star to a 440 volts, 3-phase, 50 cycles supply. Calculate the capacitance of each of the three condensers so that when they are connected in delta to the same supply the line current remains the same.

Problem 334: Three impedances, -j10, j10 and 10 ohms are wye connected. Determine the impedance of an equivalent delta.

Problem 335: A system consisting of three equal resistors connected in star is fed from a three-phase supply. By how much is the power reduced if one of the three resistors is disconnected?

Problem 336: A balanced three-phase load is wye-connected and has an impedance \(Z_P\) = 4 - j3 ohms per phase. Find the line current if this load is connected across a 220 V three-phase source.

Problem 337: Three 10-ohm resistances are connected delta on a balanced three-phase source. If the equation of the phase \(V_{an}=120\sin wt\). What is the equation of the line current in line a?

Problem 338: Given a balanced 3-wire, three-phase system serving the following loads: \(V_{ab}=200\angle0^\circ\,V\), \(Z_{ab}=10\angle53.13^\circ\,\Omega\); \(V_{bc}=200\angle240^\circ\,V\), \(Z_{bc}=10\angle0^\circ\,\Omega\); \(V_{ca}=200\angle120^\circ\,V\), \(Z_{ca}=10\angle30^\circ\,\Omega\). Determine line current on line b.

Problem 339: Given the following line voltages and two load impedances: \(V_{ab}=117\angle0^\circ\,V\), \(Z_{ac}=5+j12\,\Omega\); \(V_{bc}=117\angle240^\circ\,V\), \(Z_{bc}=13+j0\,\Omega\); \(V_{ca}=117\angle120^\circ\,V\). Solve for the line current in line c.

Problem 340: 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 lines 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging and is connected across lines 3 & 1. Find the three line currents.

Problem 341: A 120-V per phase, three-phase Y connected source delivers power to the following delta-connected load: Phase 1 = \(40\angle0^\circ\), Phase 2 = \(20\angle{-60^\circ}\), Phase 3 = \(15\angle45^\circ\). Determine the three line currents.

Problem 342: Given: \(V_{ab}=240\angle0^\circ\,V\), \(Z_{ab}=6+j8\,\Omega\); \(V_{bc}=240\angle240^\circ\,V\), \(Z_{bc}=5+j8.66\,\Omega\); \(V_{ca}=240\angle120^\circ\,V\), \(Z_{ca}=10+j0\,\Omega\). Solve for the three line currents \(I_a\), \(I_b\) and \(I_c\).