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Written for students, Principles of Analog Electronics combines theoretical background and practical examples to explain how electronic circuits work. You'll also learn about elementary analog and digital electronics, computers, and treatment of analytical datA. What is the total flux present in the air gap? An air-gap flux density of 0. A transformer core with an effective mean path length of 10 in has a turn coil wrapped around one leg. Its cross-sectional area is 0.
If current of 0.
What is the flux density? Sketch the voltage present at the terminals of the coil. This voltage will be the same polarity as the direction shown on the core, so it will be positive. Figure P shows the core of a simple dc motor. The magnetization curve for the metal in this core is given by Figure c and d.
Assume that the cross-sectional area of each air gap is 18 cm2 and that the width of each air gap is 0. The effective diameter of the rotor core is 4 cm. The relative permeability of this core is shown below: This is a design problem, and the answer presented here is not unique.
Other values could be selected for the flux density in part a , and other numbers of turns could be selected in part c. These other answers are also correct if the proper steps were followed, and if the choices were reasonable.
Notice that the saturation effects become significant for higher flux densities. Does the load consume reactive power from the source or supply it to the source?
Figure P shows a simple single-phase ac power system with three loads. The current in Loads 1 and 2 is the same as before. Since less reactive power has to be supplied by the source, the total current flow decreases. Demonstrate that Equation can be derived from Equation using simple trigonometric identities: A linear machine has a magnetic flux density of 0. What is the initial current flow? What is the efficiency of the machine under these circumstances?
A linear machine has the following characteristics: What is its final steady-state speed? What is the new steady-state speed of the bar? Reducing the flux density B of the machine increases the steady-state speed, and reducing the battery voltage VB decreases the stead-state speed of the machine. Both of these speed control methods work for real dc machines as well as for linear machines. Transformers The secondary winding of a transformer has a terminal voltage of The turns ratio of the transformer is If the secondary current of the transformer is 7.
What are its voltage regulation and efficiency? The impedances of this transformer referred to the primary side are eq 0. Since no particular equivalent circuit was specified, we are using the approximate equivalent circuit referred to the primary side. The secondary voltage and current are What is its voltage regulation?
Therefore, the secondary impedances referred to the primary side are 22 OUT cos 20 kVA 0. The results of the tests are shown below.
The resulting equivalent circuit is shown below: The rated secondary current is A A single-phase power system is shown in Figure P The load on the transformer is 90 kW at 0.
The input power supplied by the source is IN source cos V When travelers from the USA and Canada visit Europe, they encounter a different power distribution system. It has turns of wire on the V side and turns of wire on the V side. Sketch the magnetization current that would flow in the transformer. What is the rms amplitude of the magnetization current?
What percentage of full-load current is the magnetization current? The MATLAB program shown below calculates the flux level at each time, the corresponding magnetization current, and the rms value of the magnetization current. This program also The rms magnetization current is 0.
The resulting plot is This is true because the peak flux is higher for the 50 Hz waveform, driving the core further into saturation.
What is the voltage regulation of the transformer? What is its voltage regulation under these conditions? Thus the load impedance referred to the primary side is 2 The open-circuit test performed on the low-voltage side of the transformer yielded the following data: Find its efficiency. SOLUTION a The open-circuit test was performed on the low-voltage side of the transformer, so it can be used to directly find the components of the excitation branch relative to the low-voltage side.
EX The magnetizing impedance is j80 per unit. Repeat this process for power factors of 0. A program to calculate the secondary voltage of the transformer as a function of load is shown below: A three-phase transformer bank is to handle kVA and have a The kVA must be The ratings for each transformer in the bank for each connection are given below: It is supplied with power directly from a large constant-voltage bus.
SOLUTION From the short-circuit information, it is possible to determine the per-phase impedance of the transformer bank referred to the high-voltage side. Referred to the primary side of one of the transformers, the load on each transformer is equivalent to kVA at V and 0. The equivalent current flowing in the secondary of one transformer referred to the primary side is , kVA It is much easier to solve problems of this sort in the per-unit system, as we shall see in the next problem.
Calculate all of the transformer impedances referred to the low-voltage side. EQ, 0. An autotransformer is used to connect a It must be capable of handling kVA. There are three phases, connected Y-Y with their neutrals solidly grounded. The turns ratio of each autotransformer is given by SE Two phases of a A farmer along the road has a V feeder supplying kW at 0.
The single-phase loads are distributed evenly among the three phases. Also find the real and reactive powers supplied by each transformer.
Assume the transformers are ideal. From the figure, it is obvious that the secondary voltage across the transformer is V, and the secondary current in each transformer is A. The primary voltages and currents are given by the transformer turns ratios to be V and What are the transmission losses of the system? What are the transmission losses of the system now? The transformers may be assumed to be ideal.
The resistance in the transmission line is line line cos 60cos If the transformers are removed by referring the transmission line to the voltage levels found on either end, then the impedance of the transmission line becomes Also, the transmission losses in the system are reduced.
The current in the transmission line is line load 1 1 Consider the transformer to be ideal, and assume that all insulation can handle V. The transformer connection is shown below: Answer the questions of Problem for this transformer. Autotransformers are normally only used when there is a small difference between the two voltage levels.
Prove the following statement: SOLUTION The impedance of a transformer can be found by shorting the secondary winding and determining the ratio of the voltage to the current of its primary winding. For the transformer connected as an ordinary transformer, the impedance referred to the primary CN is: The open-circuit test was performed on the low-voltage side of this transformer bank, and the following data were recorded: SOLUTION a The equivalent of this three-phase transformer bank can be found just like the equivalent circuit of a single-phase transformer if we work on a per-phase bases.
The open-circuit test data on the low-voltage side can be used to find the excitation branch impedances referred to the secondary side of the transformer bank.
Since the low-voltage side of the transformer is Y-connected, the per-phase open-circuit quantities are: The per-unit voltage at the primary side of the transformer will be EQ 1.
When it is tested as a conventional transformer, the following values are measured on the primary V side of the transformer: What is the efficiency of the transformer at rated conditions and unity power factor? What is the voltage regulation at those conditions?
The core losses in resistor CR would be 22 core 1. Figure P shows a power system consisting of a three-phase V Hz generator supplying two loads through a transmission line with a pair of transformers at either end.
What is the power factor of the generator? With the switch closed? What is the effect of adding Load 2 to the system? The power system can be divided into three regions by the two transformers. The base impedances of each region will be: This problem is a good example of the advantages of power factor correction in power systems. Introduction to Power Electronics We must right a new function halfwave3 to simulate the output of a three-phase half-wave rectifier.