Scribd
Upload
382 views3 pages

Problem Set 1 Magnetic Circuits

This document contains 6 problems related to electromagnetic systems and circuits. The problems involve calculating things like maximum air gap lengths to achieve a target flux density, forces on magnetic materials, coil currents needed for a given flux density, magnetic flux in cores, effects of air gaps, and voltages and currents in transformer circuits. Calculations are shown providing the answers to each multi-part problem.

Uploaded by

Yara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
382 views3 pages

Problem Set 1 Magnetic Circuits

This document contains 6 problems related to electromagnetic systems and circuits. The problems involve calculating things like maximum air gap lengths to achieve a target flux density, forces on magnetic materials, coil currents needed for a given flux density, magnetic flux in cores, effects of air gaps, and voltages and currents in transformer circuits. Calculations are shown providing the answers to each multi-part problem.

Uploaded by

Yara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

Problem Set 1 Magnetic Circuits

1. Consider an electromagnetic system a shown below. It is used to lift a section of steel channel and it
consists of coils of 600 turns. The reluctance of the magnetic material can be neglected up to a flux
density of 1.4 T.

a. For a coil current of 15 A (DC), find the maximum air gap length at which the flux density is 1.4 T.

b. For the air gap found in (a), find the force acting on the steel channel.

2. Consider an electromagnet that can lift a length of steel strip, as shown below. It consists of 500 turns
that carry 20 A without overheating. The magnetic material consists of negligible reluctance at flux
densities up to 1.4 T. Find the maximum air gap such that a flux density of 1.4 T can be established
with a coil current of 20 A.

3. Consider a toroid that is made from cast steel with flux density of 1.2 T and field density of 1000 At/m
as shown below.

a. If a core flux density of 1.2 T at the mean radius of the toroid is needed, find the coil current.

b. Assuming uniform flux density in the coil, find the core flux in Wb.
c. If a 2-mm-wide air gap is made in the toroid, find the new coil current needed to maintain a core
flux density of 1.2 T.

4. Consider a toroid in Q.3. It consists of coil current of 2 A and relative permeability of the core of 2000.
The core is with a square cross section.

a. Find the maximum and minimum values of the flux densities in the core.

b. Find the magnetic flux in the core.

c. Find the flux density at the mean radius of the toroid and compare it with the average flux density
across the core.

5. A coil wound on a magnetic core is excited by (i) 100 V, 50 Hz and (ii) 110 V, 60 Hz. Compare the
hysteresis and eddy current losses with the two sources. For hysteresis loss, n = 2 is chosen.

6. Consider a two-winding transformer with a laminated core as shown below. It consists of primary
winding of 200 turns that is able to generate a flux density in the core of B = 1.2 sin 377 t. The
secondary winding consists of 400 turns that is left open-circuited. The stacking factor of the core is
0.95, i.e., the core occupies 95 % of the gross core volume. The gross cross-sectional area of the core
is 25 cm2 with relative permeability of 10,000. The core length is 90 cm.

a. Find the rms value of the applied voltage.

b. Find the current in the winding.

c. Find the rms voltage induced in the secondary winding.


Answer

1. (a) 4.04 mm (b) 199.6 kN

2. 4.5 mm

3. (a) 2.51 A (b) 1.51 x 10-3 Wb (c) 12.1 A

4. (a) 2.67 T; 1.6 T (b) 3.27 x 10-3 Wb (c) 2 T; 2.04 T

5. 1.008; 1.21

6. (a) 152 V (b) i1 = 0.43 sin 377 t (c) 304 V

You might also like