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Sinusoidal voltage applied to the coil with ferromagnetic core

# TECircuit1: Coil with ferromagnetic core

This is an example of the coil with ferromagnetic core simulation, performed with QuickField software.

**Problem Type:**

Axisymmetric problem of transient magnetics.

**Geometry:**

Due to the model symmetry only the right half of the coil is presented in the model (shown by upper half of its cross-section). Therefore the circuit elements' values are defined twice less than in the real object.

**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 (amplitude) *U* = 10*sqrt(2) V;

Frequency *f* = 50 Hz.

**Problem:**

Determine the electric current within the coil winding.

**Solution:**

The current wave period is T = 1 / f = 0.02 sec. We choose the time step of 0.0005 second that guarantees a smooth plot. The finishing time 0.2 sec includes 10 periods and is long enough to fade out initial transient currents. To reduce the results file size only the last period is stored (starting from moment 0.18 sec).

**Results:**

The current in the winding is: *I(t)* = 59.6·cos(*t*·2π/T - 166°)

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