Consider the magnetic circuit of Figure. This structure, known as a pot-core, is typically made in two halves. The N-turn coil is wound on a cylindrical bobbin and can be easily inserted over the central post of the core as the two halves are assembled. Because the air gap is internal to the core, provided the core is not driven excessively into saturation, relatively little magnetic flux will "leak" from the core, making this a particularly attractive configuration for a wide variety of applications, both for inductors such as that of Figure and transformers. Assume the core permeability to be ? = 2500 ?0 and N = 200 turns. The following dimensions are specified: R1 = 1.5cm R2 = 4cm l = 2.5cm h = 0.75cm g = 0.5mm

a. Find the value of R3 such that the flux density in the outer wall of the core is equal to that within the central cylinder.

b. Although the flux density in the radial sections of the core (the sections of thickness h) actually decreases with radius, assume that the flux density remains uniform. (i) Write an expression for the coil inductance and (ii) evaluate it for the given dimensions.

c. The core is to be operated at a peak flux density of 0.8 T at a frequency of 60 Hz. Find (i) the corresponding rms value of the voltage induced in the winding, (ii) the rms coil current, and (iii) the peak stored energy.

d. Repeat part (c) for a frequency of 50 Hz.

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Core: mean length le area A. relative permeability 4, N-turn coil СЛ. N-turn winding R2 R3