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- Question : 1E - The long solenoid coil shown in Fig. P1.1 has 250 turns. As its length is much greater than its diameter, the ?eld inside the coil may be considered uniform. Neglect the ?eld outside. (a) Determine the ?eld intensity (H) and ?ux density (B) inside the solenoid (i = 100 A). (b) Determine the inductance of the solenoid coil.
- Question : 2E - In the magnetic system of Fig. P1.2 two sides are thicker than the other two sides. The depth of the core is 10 cm, the relative permeability of the core ?r = 2000, the number of turns N = 300, and the current ?owing through the coil is i = 1 A. (a) Determine the ?ux in the core. (b) Determine the ?ux densities in the parts of the core.
- Question : 3E - For the magnetic system of Problem 1.2, ?nd the current i in the coil to produce a ?ux ? = 0:012 Wb.
- Question : 4E - Two coils are wound on a toroidal core as shown in Fig. P1.4. The core is made of silicon sheet steel and has a square cross section. The coil currents are i1 = 0:28 A and i2 = 0:56 A. (a) Determine the ?ux density at the mean radius of the core. (b) Assuming constant ?ux density (same as at the mean radius) over the cross section of the core, determine the ?ux in the core. (c) Determine the relative permeability, ?r, of the core.
- Question : 5E - The magnetic circuit of Fig. P1.5 provides ?ux in the two air gaps. The coils (N1 = 700, N2 = 200) are connected in series and carry a current of 0.5 ampere. Neglect leakage ?ux, reluctance of the iron (i.e., in?nite permeability), and fringing at the air gaps. Determine the ?ux and ?ux density in the air gaps.
- Question : 6E - A two-pole generator, as shown in Fig. P1.6, has a magnetic circuit with the following dimensions: Each pole (cast steel): magnetic length = 10 cm cross section = 400 cm2 Each air gap: length = 0:1 cm cross section = 400 cm2 Armature (Si-steel): average length = 20 cm average cross section = 400 cm2 Yoke (cast steel): mean circumference = 160 cm average cross section = 200 cm2 Half the exciting ampere-turns are placed on each of the two poles. (a) Draw the magnetic equivalent circuit. (b) How many ampere-turns per pole are required to produce a ?ux density of 1.1 tesla in the magnetic circuit. (Use the magnetization curves for the respective materials.) (c) Calculate the armature ?ux.
- Question : 7E - A two-pole synchronous machine, as shown in Fig. P1.7, has the following dimensions: Each air gap length, lg = 2:5 mm Cross-sectional area of pole face, Ag = 500 cm2 N = 500 turns I = 5A ?c = infinity (a) Draw the magnetic equivalent circuit. (b) Find the ?ux density in the air gap.
- Question : 8E - The electromagnet shown in Fig. P1.8 can be used to lift a length of steel strip. The coil has 500 turns and can carry a current of 20 amps without overheating. The magnetic material has negligible reluctance at ?ux densities up to 1.4 tesla. Determine the maximum air gap for which a ?ux density of 1.4 tesla can be established with a coil current of 20 amps. Neglect magnetic leakage and fringing of ?ux at the air gap.
- Question : 9E - The toroidal (circular cross section) core shown in Fig. P1.9 is made from cast steel. (a) Calculate the coil current required to produce a core ?ux density of 1.2 tesla at the mean radius of the toroid. (b) What is the core ?ux, in webers? Assume uniform ?ux density in the core. (c) If a 2-mm-wide air gap is made in the toroid (across A?A0 ), determine the new coil current required to maintain a core ?ux density of 1.2 tesla.
- Question : 10E - In the toroidal core coil system of Fig. P1.9, the coil current is 2:0 A and the relative permeability of the core is 2000. The core has a square cross section. (a) Determine the maximum and minimum values of the ?ux density in the core. (b) Determine the magnetic ?ux in the core. (c) Determine the ?ux density at the mean radius of the toroid, and compare it with the average ?ux density across the core.
- Question : 11E - The magnetic circuit of Fig. P1.11 has a core of relative permeability ?r = 2000. The depth of the core is 5 cm. The coil has 400 turns and carries a current of 1:5 A. (a) Draw the magnetic equivalent circuit. (b) Find the ?ux and the ?ux density in the core. (c) Determine the inductance of the coil.
- Question : 12E - Repeat Problem 1.11 for a 1.0-cm-wide air gap in the core. Assume a 10% increase in the effective cross-sectional area of the air gap due to fringing in the air gap.
- Question : 13E - The magnetic circuit of Fig. 1.9 has the following parameters: N = 100 turns Ac = Ag = 5 cm2 ?core = infinity Determine the air gap length, lg, to provide a coil inductance of 10 mH.
- Question : 14E - An inductor is made of two coils, A and B, having 350 and 150 turns, respectively. The coils are wound on a cast steel core and in directions as shown in Fig. P1.14. The two coils are connected in series to a dc voltage. (a) Determine the two possible values of current required in the coils to establish a ?ux density of 0:5 T in the air gap. (b) Determine the self-inductances LA and LB of the two coils. Neglect magnetic leakage and fringing. (c) If coil B is now disconnected and the current in coil A is adjusted to 2:0 A, determine the mean ?ux density in the air gap.
- Question : 15E - The magnetic circuit for a saturable reactor is shown in Fig. P1.15. The B?H curve for the core material can be approximated as two straight lines as in Fig. P1.15. (a) If I1 = 2:0 A, calculate the value of I2 required to produce a ?ux density of 0:6 T in the vertical limbs. (b) If I1 = 0:5 A and I2 = 1:96 A, calculate the total ?ux in the core. Neglect magnetic leakage. (Hint: Trial-and-error method.)
- Question : 16E - A toroidal core has a rectangular cross section as shown in Fig. P1.16a. It is wound with a coil having 100 turns. The B?H characteristic of the core may be represented by the linearized magnetization curve of Fig. P1.16b. (a) Determine the inductance of the coil if the ?ux density in any part of the core is below 1:0 Wb=m2. (b) Determine the maximum value of the current for the condition of part (a). (c) Determine the minimum value of the current for which the complete core has a ?ux density of 1:0 Wb=m2 or greater.
- Question : 17E - A coil wound on a magnetic core is excited by the following voltage sources. (a) 100 V, 50 Hz. (b) 110 V, 60 Hz. Compare the hysteresis losses and eddy current losses with these two different sources. For hysteresis loss, consider n = 2.
- Question : 18E - A toroidal core of mean length 15 cm and cross-sectional area 10 cm2 has a uniformly distributed winding of 300 turns. The B?H characteristic of the core can be assumed to be of rectangular form, as shown in Fig. P1.18. The coil is connected to a 100 V, 400 Hz supply. Determine the hysteresis loss in the core.
- Question : 19E - The core in Fig. 1.17 has the following dimensions: cross-sectional area Ac = 5 cm2, mean magnetic path length lc = 25 cm. The core material is silicon sheet steel. If the coil has 500 turns and negligible resistance, determine the rms value of the 60 Hz voltage applied to the coil that will produce a peak ?ux density of 1:2 T.
- Question : 20E - Figure P1.20 shows a two-winding transformer with a laminated core. The winding with N1 = 200 turns is connected to a voltage to produce a ?ux density in the core B = 1:2 sin 377t. The second winding, with N2 = 400 turns, is left open-circuited. The stacking factor of the core is 0.95
- Question : 21E - The ?ux in the core of the magnetic system of Fig. 1.17 varies with time as shown in Fig. P1.21. The coil has 400 turns. Sketch the waveform of the induced voltage, e, in the coil.
- Question : 22E - A six-step voltage of frequency 60 Hz, as shown in Fig. P1.22, is applied on a coil wound on a magnetic core. The coil has 500 turns. Find the maximum value of the ?ux and sketch the waveforms of voltage and ?ux as a function of time.
- Question : 23E - In the circuit of Fig. P1.23a, a resistanceless toroidal winding of 1000 turns is wound on a ferromagnetic toroid of cross-sectional area 2 cm2. The core is characterized by the ideal B?H relation shown in Fig. P1.23b. This circuit is excited by a 60 Hz square wave of input voltage (vi) of amplitude 108 volts, as shown in Fig. P1.23c. Determine the switching instant and sketch the waveforms of the voltages vL and vo.
- Question : 24E - Suppose that the soft iron keeper in the permanent magnet of Example 1.8 is reinserted. Determine the ?ux density in the magnet if the recoil permeability (?rec) of the magnetic material is 4?0.
- Question : 25E - Repeat Example 1.8 if the permanent magnet material is samarium
- Question : 26E - Repeat Problem 1.25 if the permanent magnet material is neodymium

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