1-Phase AC Circuits

Problem 235: A series circuit composed of a 0.2 henry inductor and a 74-microfarad capacitor is connected to a 60 V variable frequency source. At what frequency is the current be 4 amperes with a lagging power factor?

Problem 236: A single phase lagging power factor load takes 300 W and 5 A at 120 V. Find the reactance of a pure capacitor that maybe placed in series with this load so that it will operate normally from a 240-V source.

Problem 237: A coil (RL) is connected in series with a capacitor across a 220 V, 60 Hz AC supply. The circuit is designed such that the voltage across the coil and the capacitor are numerically equal. If this circuit operates at 0.87 leading pf, determine the magnitude of this voltage.

Problem 238: A series circuit connected across a 100-V AC source consists of a 10-\(\Omega\) resistor, a 5-\(\Omega\) capacitor, a resistance R that takes 50 W and a reactance X taking 100 inductive VARS. Determine the minimum value of current required satisfying the above conditions.

Problem 239: The maximum instantaneous voltage and current outputs of an alternator are 300 V and 20 A, respectively. What is the power output in watts if the voltage leads the current by 30°?

Problem 240: A 50-microfarad is connected in series with a coil having 50 ohms resistance and 150-mH inductance. The source voltage is 100 sin (wt - 30°) V. What is the maximum power?

Problem 241: An impedance draws a current i = 10 cos (wt - 30°) from a voltage v = 220 sin wt. What is the maximum power?

Problem 242: An incandescent lamp load generally considered to be made up of resistors take 4.8 kW from a 120-V AC source. The instantaneous maximum value of power is

Problem 243: A circuit consists of \(X_L\) = j5 ohms, \(X_C\) = -j5 ohms and R = 5 ohms all are connected in parallel. Find the equivalent impedance.

Problem 244: Given: \(Z_1\) = -j2.5 ohms; \(Z_2\) = j4 ohms; \(Z_3\) = 5 ohms; \(Z_4\) = 1 + j5 ohms. If the four impedances are connected in parallel, find the equivalent impedance in ohms.

Problem 245: Three impedances \(Z_a\) = 3 + j4 ohms, \(Z_c\) = 4 - j4 ohms and \(Z_r\) = 0 + j3 ohms are connected in parallel. Solve for the pf of the combination.

Problem 246: A pure capacitance of \(530.515\times10^{-6}\) farad and an inductance of \(530.515\times10^{-4}\) henry are connected in parallel across an AC power source. Solve for their resultant impedance assuming that the frequency is 30 Hz.

Problem 247: A coil of a 50-ohm resistance and of 150 mH inductance is connected in parallel with a 50 \(\mu F\) capacitor. What is the power factor of the circuit?

Problem 248: Three impedances \(Z_a\), \(Z_c\), \(Z_r\) are connected in parallel. If at 60 Hz, \(Z_a\) = 0 + j8, \(Z_c\) = 0 - j2 and \(Z_r\) = 5 + j0 ohms. Solve for the resultant power factor.

Problem 249: A resistor of 50 ohms and an impedance of 100 + j50 ohms are connected in parallel across a 220 volts supply. What is the power factor of the load?

Problem 250: A capacitor, an electric resistance heater, and an impedance are connected in parallel to a 120 V, 60 Hz system. The capacitor draws 50 VAR, the heater draws 100 W and the impedance coil draws 269 VA at a pf of 0.74 lagging. Determine the system power factor.

Problem 251: A given load takes 40 kVA at 50% lagging power factor, while another load connected in parallel across the same source takes 80 kVA at 86.7% lagging power factor. Find the apparent power.

Problem 252: A 440 V, 60 Hz generator, supplies two parallel-connected loads A and B. 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 kVAR supplied by the generator.

Problem 253: Two single-phase motors are connected in parallel across a 120-volt, 60-cycle source of supply. Motor A is a split-phase induction type and motor B is a capacitor type: A (1/4 hp, 0.60 eff, 0.7 lag), B (1/2 hp, 0.70 eff, 0.95 lag). Determine total power factor.

Problem 254: A 250-kVA, 0.5 lagging power factor load is connected in parallel to a 180-W, 0.8 leading power factor load and to a 300-VA, 100 VAR inductive load. Determine the total apparent power in kVA.