Concept explainers
A 240-V rms 60-Hz supply serves a load that is 10 kW (resistive), 15 kVAR (capacitive), and 22 kVAR (inductive). Find:
- (a) the apparent power
- (b) the current drawn from the supply
- (c) the kVAR rating and capacitance required to improve the power factor to 0.96 lagging
- (d) the current drawn from the supply under the new power-factor conditions
(a)
Find the apparent power for the given loads.
Answer to Problem 73P
The apparent power for the given loads is
Explanation of Solution
Given data:
The voltage
The Frequency
The real power
The reactive power is,
Formula used:
Write the expression to find the complex power.
Here,
Calculation:
Substitute
As the reactive power
On comparing the above equation with equation (1).
The apparent power
Conclusion:
Thus, the apparent power for the given loads is
(b)
Find the current drawn from the supply.
Answer to Problem 73P
The current drawn from the supply is
Explanation of Solution
Given data:
From Part (a), the complex power is,
The voltage
Formula used:
Write the expression to find the rms current.
Calculation:
Substitute
Convert the equation from rectangular to polar form.
Conclusion:
Thus, the current drawn from the supply is
(c)
Find the value of the capacitance and reactive power to raise the power factor to 0.96 lagging.
Answer to Problem 73P
The value of capacitance C is
Explanation of Solution
Given data:
From Part (a),
The frequency
Power factor
The rms voltage is
Formula used:
Write the expression to find the phase angle
Here,
Write the expression for phase angle
Write the expression to find the value of the capacitance.
Here,
Calculation:
Substitute
The power factor is raised to 0.96 lagging.
Substitute 0.96 for
The reactive power is calculated as follows.
Substitute
Substitute
Simplify the equation as follows,
Conclusion:
Thus, the value of capacitance C is
(d)
Find the current drawn from the supply under the new power factor condition.
Answer to Problem 73P
The current drawn from the supply is
Explanation of Solution
Given data:
The voltage
The real power is,
From Part (a),
From Part (c),
Calculation:
The complex power
The reactive power
Substitute
Substitute
Substitute
Convert the equation from rectangular to polar form.
Conclusion:
Thus, the current drawn from the supply is
Want to see more full solutions like this?
Chapter 11 Solutions
FUND.OF ELECTRIC CIRCUIT(LL)-PACKAGE
- What is the equation of the current in B in the function of sin given that Two electric devices A and B are connected in parallel, and the rms current in A is 15 amp. If the current in B lags behind A by π/3 radians and the total linecurrent is 23.4 amp. (rms).arrow_forwardA 40 Ω resistor, a 200 μF capacitor and a 269 mH inductor are connected in series across a voltage source represented by: V = 163.34 sin(100t) volts Determine the following: A.) The rms value of current is A. (a) 0.75 (b) 1.5 (c) 2.5 (d) 3.5 B.) The total impedance of the circuit is ohms. a.) 46.19 b.) 54.37 c.) 65.15 d.) 32.65 C.) The real power supplied is watts (a) 144.35 (b) 125 (c) 175.25 (d) 250 D.) The power factor of the circuit is . (a) 0.707 lagging (b) 0.866 leading (c) 0.6 leading (d) 0.5 laggingarrow_forwardThe load at a certain factory consists of the following:10 kW, pf = 0.6 lagging15 kW, rf = 0.5 lagging25 kVA, pf = 0.75 lagging15 kVAR, pf = 0.8 lagging22 kW5 kVAR, pure inductance1. The power factor is to be corrected to 0.95 lagging. Determine the kVAR rating of pure capacitors needed to accomplish this.arrow_forward
- A factory has a large induction heater operating at 1000 V, 50Hz. The current flowing intothe heater is 12.33 A RMS and the true power is 10 kW b) Calculate the reactive power, apparent power and the power factor (PF) for this load.c) If the PF is lower than 0.9, explain the problem from an electrical perspective thencalculate how this load could be balanced practically.d) Draw a diagram to illustrate where the capacitor needs to be placed and what hashappened to the reactive current that was originally flowing from the inductive load backto the supplier? What are the specifications for this capacitor? What would such acapacitor cost? Who could supply this type of component?arrow_forwardA sawmill uses a 15-hp electric motor operating at 480 V rms. Its power factor is 0.82. When a power-factor-correcting capacitor is added to the system, the power factor increases to 0.95. Find the rms current in the wires supplying the motor a) before and b) after the power factor increase.arrow_forwardA motor draws 680 W at 156 Vrms 60Hz. The motor is operating at a lagging power factor, with a power factor angle of 45 deg.. Determine the capacitance (in microFarad) required to correct the power factor so that the power factor angle becomes 15 deg, lagging. (Give answer in 2 decimal places. Unit is not required)arrow_forward
- The power of a certain CD player operating at 120 V rms is20.0 W. Assuming that the CD player behaves like a pure resistor, find the maximum instantaneous powerarrow_forwardA circuit branch is found to have an equivalent impedance of Z=120−j45Ω. It is given that this impedance is a series combination of a 120Ω resistor and another passive component. If the circuit has a sinusoidal voltage source whose frequency is 120 Hz. What is the value of the component in series with the 120Ω resistor? (Note: Express the value assuming a metric scaling of μ(10-6). Provide your answer in decimal form, up to 3 decimal places.)arrow_forwardA power station supplies the following loads to various consumers: Industrial consumer = 1500kW Commercial establishment = 750kW Domestic power = 100kW Domestic light = 450kW If the maximum demand on the station is 2500kW and the number of KWh generated per year is 45x105. Determine the diversity factor The annual load factorarrow_forward
- A source whose voltage is ? (?) = 50√2 cos (?? + 30 °) ? supplies a load of impedance ? = (4 + ?3) Ω. We want to know: a) the active, reactive and apparent power consumed by the load. b) the power of a capacitor that must be installed in parallel with the load to raise its power factor to 0.97 delayed.arrow_forwardYou own a factory that uses several conveyor belts and other motor-driven machineries. Upon measuring the factory's apparent power requirement and power factor, it turns out that it runs at 15 MVA at 0.7 lagging of; therefore, it is too inductive! To avoid electrical code violations, the factory must operate at a pf of at least 0.9 lagging. If the factory is connected to 34.5 kV AC at 60 Hz, what is the size of the compensating capacitor that must be installed to achieve the desired pf level? Express the answer in microfarads. The given voltage can be assumed to be at angle zero.arrow_forwardHelp me please IN THE CIRCUIT SHOWN, THE VALUE OF THE CURRENT SOURCE IS IN RMS VALUE. DETERMINE: A) THE VOLTAGE (ONLY THE MAGNITUDE) AT THE INDUCTOR TERMINALS, VL B) THE VOLTAGE (ONLY THE MAGNITUDE) AT THE RESISTOR TERMINALS, VR C) THE AVERAGE POWER ABSORBED BY THE 40 Ω RESISTORarrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,