In a power converter design it is required the use a 1 mH inductor to be able to

Question

In a power converter design it is required the use a 1 mH inductor to be able to supply 1 A to a load. As an engineer you are required to design this inductor using the core shown in the figure. Determine: Determine the required number of turns to be able to construct an inductor of 1 mH. What would be the magnetomotive force in the winding? What would be the magnetic flux density in the air gab? What would be the maximum amount of energy this inductor can store? A 30-turn rectangular coil with sides I = 15 cm and w = 25 cm is placed in the y-z plane with one of its sides hinge over the z-axis, if the coil, which carries a current of 25 A (when the coil is over the y-z axis, the current is flowing counterclockwise) is in the presence of a magnetic flux density B = 15(3x - y) T. Determine: The torque T(phi) acting on the coil. At what angle (phi) is the torque zero? At what angle phi is the torque maximum? Determine its value. What would be the magnetic moment of the loop? Show that the mutual inductance between the rectangular loop of N-turns and an infinite line current of the figure is: M_12 = N mu b/2 pi ln (a + r_0/r) Calculate M12 when a = 5 cm, r_0 = 20 cm, b = 30 cm. N = 20 turns, and the medium is free space. Determine the magnetic flux linking the loop if the current flowing through the wire is 20 A.

Explanation / Answer

1

1) . L = mu0N2A / l

mu0 = 4 *3.14 *10-7

A = 3.14*r2 = 3.14 * 1 = 3.14 cm2

therefor 1*10-3 = 4*3.14*10-7*N2 *3.14*10-4/ 2 *10-2

N = 225turns

2).L = Nphi / i

phi =4.44*10-6 wb

Magnetomotive force = phi * Rc = phi * lc/(mu0 *mur * Ac)

mur= 2000mu0

F = 4.44 *10-6 * 2*10-2/(2000*(4* 3.14* 10 -7)2 * 3.14* 10-4

=8.96*10-4N

3).Phi = B*Ag = B*4*10-6

B =1.11T

4) Energy stored = 0.5Li2 = 0.5*10-3W

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