Concept explainers
For the circuit in Fig. 11.47, find the value of ZL that will receive the maximum power from the circuit. Then calculate the power delivered to the load ZL.
Find the value of the load impedance
Answer to Problem 16P
The value of load impedance
Explanation of Solution
Given data:
Refer to Figure 11.47 in the textbook.
The inductance
The capacitance C is
The source voltage is
Formula used:
Write the general expression for the instantaneous voltage.
Write the expression to find the maximum average power.
Here,
Write the expression for
Calculation:
On comparing equation (1) and (2), the angular frequency is,
Write the expression for the reactance of the inductance.
Substitute
Write the expression for the reactance of the capacitance.
Substitute
Refer to Figure 11.47 in the textbook.
To find the Thevenin equivalent the given Figure is modified as shown in Figure 1.
In Figure 1, apply Kirchhoff’s currrent law at node voltage
Rearrange the equation as follows,
In Figure 1, apply Kirchhoff’s currrent law at node voltage
Rearrange the equation as follows,
Substitute equation (6) in equation (5).
Rearrange the equation as follows,
The voltage voltage
Convert the equation from rectangular to polar form.
The Thevenin voltage is,
In Figure 1, to calculate the Thevenin impedance
In Figure 2, apply Kirchhoff’current law at node voltage
Rearrange the equation as follows,
In Figure 2, apply Kirchhoff’current law at node voltage
Rearrange the equation as follows,
Substitute equation (7) in equation (8).
Rearrange the equation as follows,
Convert the equation from rectangular to polar form.
The Thevenin impedance
Substitute
Convert the equation from polar to rectangular form.
For maximum average power transfer, the load impedance
Convert the equation from rectangular to polar form.
On comparing the equation (9) with equation (4).
Substitute
Conclusion:
Thus, the value of load impedance
Want to see more full solutions like this?
Chapter 11 Solutions
Fundamentals of Electric Circuits
- For the circuit in Fig. 11.47, find the value of ZL that will receive the maximum power from the circuit. Then calculate the power delivered to the load ZL.arrow_forwardTwo loads Z1 = 70+j80 ohms and Z2 = 20+ j 30 ohms are connected across 240V, 50Hz supply. Find the total current flowing in the circuit.How power factor will be improved after connecting 75.6 micro farad capacitor across the load. What can you infer from the result?arrow_forwardA 1500 kvA, 3Φ star-connected alternator, 50 Hz,2300 V alternator has a resistance between each pair of terminals as measured by direct currents is 0.16 ohm. Assume that the effective resistance is 1.5 times the ohmic value. A field current of 70 A produces a short-circuit current equal to full load current of 376 A in each line. The same field current produces an emf of 700 V on open circuit. Determine the synchronous reactance of the machine and its full load voltage regulation at 0.8 power factor lagging. [Ans. VR = 22.8 %]arrow_forward
- For the circuit of Fig.11.78 composed of standard values: A. Determine the time constant. B. Write the mathematical expression for the current It after the switch is closed C. Repeat part (b) for VL and VR D. Determine il and VL at one three- and five-time constants. E. Sketch the waveforms of iL,VL and VR.arrow_forwardSHOW COMPLETE SOLUTION. A. Determine the resistance component of Load 2. Use ohm's law and two decimal places. B. A capacitor will be connected in parallel with the source and the loads. What must be the value of this capacitor in microfarads to increase the overall power factor seen by the source to unity or 1.0? Use two decimal places.arrow_forwardb) A 250V is used to supply a 20kW load at 50HZ with leading power factor of 0.75. Determine the following : ii. State whether this load is generating or consuming reactive power.arrow_forward
- 3. A power station has a quarterly energy output of 11,100,000 kWh. Its utilization factor is 80% and the reserve over the peak load is 4000 kW. The rated capacity of the plant is. kW.arrow_forwardAn automotive alternator is rated 500 VA and20 V. It delivers its rated voltamperes at a powerfactor of 0.85. The resistance per phase is 0.05Ω , andthe field takes 2 A at 12 V. If the friction and windageloss is 25 W and the core loss is 30 W, calculate thepercent efficiency under rated conditions.arrow_forwarda) Explain briefly how electricity can be sold to a grid by use solar energy. b) Wind farm consist of ten wind turbines with nominal capacity of 2MWper turbine, has a total of 20 MW for farm as a whole, in year 2020, the farm produced a total energy 43416MWH, find a capacity factor.arrow_forward
- 6. An 8 pole, 30 diesel generator has a line voltage of 450V at 62.5 Hz when its circuit breaker is open. At full load it supplies a line current of 410 Amps at a power factor of 0.83 lagging, its line voltage droops to 440V and the frequency droops to 60.0 Hz. The generator's full load efficiency is 85%. The efficiency of the diesel engine is 36%. a) What is the generator's % voltage regulation? b) What is the diesel engine's no load speed RPM, its full load speed RPM and its % speed regulation? c) What is the alternator's output apparent kVA, active kW, and reactive kvar power at full load? d) What is the full load output power in horsepower and shaft torque in kNm of the diesel engine? e) What are the power losses in the generator and diesel in kW? f) The diesel burns heavy fuel oil with a calorific value of 40.7 MJ/kg. Estimate the engine's fuel consumption in kg/hour at full load.arrow_forwardA 75MW power plant has an average load of 35000kW and a load factor of 65%. Find the reserved carried over and above peak loadarrow_forwardA) An energy meter whose constant is 1500 reVolutions per KWh makes, 20 reVolutions in 30 seconds. Calculate the load inKW. B) 230V single phase energy meter has constant load current of(4Apassing through it, fort hours at unity power factor. If the meter makes 1104 revolutions during this period, what is the meter constant? If the load power is 0.8 ,then what will be the number of revolutions of the disc in the above time?arrow_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,