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TEMagn2: Transient eddy currents in a two-wire line
This is an example of the two-wire line simulation, performed with QuickField software.
Problem Type:
A plane problem of nonlinear transient magnetics.
Geometry:
Transmission line consists of two copper conductors with equal but opposite currents. All dimensions are in millimeters.
Given:
Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper g = 56,000,000 S/m;
Voltage applied U = 0.001 V;
Problem:
Clculate the transient currents within the conductors.
Solution:
The resistance of one conductor can be calculated as Rcond = l / (g · S),
where
S = πr2 - cross-section area of conductor,
r - radius of conductor,
l - length of the line.
Rcond = 1 / (56·106 · (π·0.00012)) = 0.5684 Ohm
The resistance of both conductors is R = 2·Rcond = 2·0.5684 = 1.1368 Ohm
The inductunce of the transmission line can be calculated as L = μ0·l/π · (ln(D/r) + 0.25),
where
D - distance between conductors.
L = 4π·10-7·1/π · (ln(0.02/0.0001) + 0.25) = 2.219·10-6 Hn
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The transient current for eqiuvalent electric circuit with lumped parameter is
described by the formula
I(t) = U/R · (1 - e—t/T), where T=L/R - characteristic time of the circuit.
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Results:
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