A twocoil system has the same selfinductances ie L1 L2 Its

A two-coil system has the same self-inductances, i.e., L_1 = L_2. Its coupling coefficient is given by k = 0.4. Suppose that coil #2 is open and demands an output voltage v_2(t) = 60 sin(120 pi t) v. If the input voltage is v_1(t), find the voltage ratio a = v_1/v_2; What is the required input voltage v_1(t) on coil #1? If the two coils are connected in series with the total inductance L = 7 H., determine L_1, L_2 and the mutual inductance M. An AC circuit with an ideal transformer is shown in Figure. Suppose that R_1 = 100 K ohm, R_2 = 5 K ohm, C_2 = 20 mu F, and the ideal transformer has a turns ratio a = N_1/N_2. Drew an equivalent circuit without ideal transformer, and show the value of each component; If we wish the entire circuit connected to the voltage source would have a time constant T = RC = 0.18 seconds, find the necessary turns ratio a; If v_1 = 20 sin(10t) v. is applied as a voltage source as the input, find the output voltage phasor across C_2. A load impedance is given by Z = 100 - 50 squareroot 3j in ohm. An AC voltage is applied on the load impedance with a current I = 4 Amps in rms value. Find the apparent power S; Find the power factor p.f. and indicate leading or lagging. Determine the real power P, What is the reactive power Q?

Solution

Brushless dc motors initially were designed in large numbers for spindle drives in Winchester disk drives. The early designs were three-phase, later moving to two-phase and then one-phase, due to the very slow start-up requirements, very small friction loads, and the need to reduce unit cost at all levels. The industrial and machine tool markets started with and continue to use three-phase BLDC motors in their variable-speed, variable-load, high-start-up applications. The overwhelming popularity of three-phase BLDC motors focuses this subsection toward three-phase windings. Many of the initial design activities for various winding patterns can be traced back to the 1920s and earlier based on work done on three-phase ac windings.
This subsection reviews the various winding line connections, the key winding patterns and hookups, various winding constants, and winding selection and design techniques.
Basic Winding Configurations. There are other basic decisions that must be made by the design engineer before a BLDC motor design can commence. Previously defined is the number of phases, which is three here. Next in importance is the number of poles. The use of two poles is waning, and the use of six or eight poles is increasing. Four-pole BLDC motors are among the most popular used today. Two-and four-pole BLDC motor designs are used here, but the rules for two and four poles can be extended to higher pole counts. The number of stator slots (and teeth) and the winding pattern are key design decisions. This section is dedicated to reviewing the important parameters of these two design decisions.
In a three-phase motor there are three windings or phases positioned 120° electrical apart. Figure 5.30 shows the location of 6 coils in a representative 12-slot sta-tor. A two-pole rotor (not shown) will rotate as the three windings are energized in sequence A-B-C, as A-A’, B-B’, and then C-C are energized sequentially.The three-phase winding always develops positive