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# Coil with ferromagnetic core

Sinusoidal voltage is applied to the electric coil with ferromagnetic core.

Problem Type:
Axisymmetric problem of AC magnetics.

Geometry:

Given:
Magnetic permeability of the steel core μ - nonlinear;
Conductivity of the steel core g = 10,000,000 S/m;
Magnetic permeability of the winding μ = 1;
Conductivity of the winding (copper) g = 56,000,000 S/m;
Number of turns w = 120;
Applied voltage value U = 13.33 V;
Frequency f = 50 Hz.

Problem:
Determine the electric current within the coil winding.

Solution:
Due to the model symmetry only half of the coil is presented in the model. Therefore the circuit elements' values are defined twice less than in the real object.
Current vs time plot in the real coil has non-sinusoidal shape (see TECircuit1 example). With AC magnetics module we can estimate RMS value much faster. The drawback of this approach is that we cannot estimate true wave form.

Results:
AC current waveform in the coil Problem Current (RMS value), A Current (wave form), A Transient 34.1 48.1·sin(wt + 108°) + 3.2·sin(3wt + 147°) + 1·sin(5wt + 177°) AC magnetics 35.3 49.9·sin(wt + 104°)
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