Homework # 2 EE517 Fall 2000 Due September 7, 2000
Start reading chapter 2 in Woodson & Melcher
The potential in a given region is .
The iron's core has the same cross section everywhere.
For the magnetic core above ht is 0.25 inches, OR = 2.5 inches, and IR = 1.5 inches. The relative permeability of the material is 100 and there are 50 turns wound on the core. Be sure to label your units. Obtain an exact solution taking advantage of the problem's symmetry.
a) If the winding current is 30 A dc, what are the maximum H field and the maximum B field in the core and where in the core do they occur? Where in the core is the field a minimum?
b) The saturation flux density of a common magnetic iron, 3.25 % SiFe, is 1.6 Tesla. At what current will the above core begin to saturate?
c) Draw the contour and surface for using Faraday's law to find the voltage at the terminals of this inductor.
d) What is the inductance of this inductor and what is the flux (l) linked by the winding with a current of 30A?
e) What is the voltage at the terminals of the winding for 30A dc and for 60Hz 30A peak ac?
f) What is the current density in the wire for 30A dc if you assume the wire occupies all the space available to it and you neglect the space between the different turns?
g) What do you think happens in a circuit when the core saturates, i.e. the B field becomes a constant value? What is the circuit model for the inductor in this case.