Electric circuit analysis - QuickField simulation example
QuickField offers an opportunity to include an electric circuit into the analyzed model. This example demonstrates the accuracy of the embedded circuit simulation.
How to calculate currents, voltages, and power balance in an AC circuit?
Answer Typical applications Geometry Given Task Solution Total power is determined as S = U * I' = P + i*Q, Results
Complex power in voltage source V Measured RMS values of voltages and currents, average values of powers.
Power balance
*Mathematical Methods for Physicists. A Comprehensive Guide. 7th Edition. George Arfken, Hans Weber, Frank Harris, p 937-938. ISBN 978-0-12-384654-9.
Engineering question
Solve the AC circuit, read the RMS currents and voltages and complex power for each element, and verify that the total active and reactive power balance is zero.
AC electric circuits, coupled circuit networks, educational circuit examples
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Simulation problem
Problem Type
Plane-parallel problem of AC Magnetics.
As it is explained in the Solution section below, the field model geometry is not affecting the circuit simulation. Here is the circuit schema.
R = 20 Ohm
XL = 10 Ohm
XC = 2 Ohm
Current source I = 4 A (RMS) @ 0°
Voltage source U = 60 V (RMS) @ 30°
Frequency f = 50 Hz
Currents, voltages, and complex power in a linear AC circuit containing resistive, inductive, capacitive, voltage-source, and current-source elements.
QuickField could solve only coupled field-circuit problems, and the field problem should be AC or Transient Magnetic. So we created fictitious AC Magnetic problem with one block, not connected to the circuit, just to agree with this requirement. All following considerations and results relate to the circuit simulation only.
where U - voltage [V],
I' - complex conjugate of current [A],
P - average active power [W],
Q - reactive power [V·Ar].
S(V) = 60@30° * 10.58@(-79.1°) = 634.8@(-49.1°) = 415.6 - i*479.8 [V·A].
Voltage V, V
Current I, A
Real power P, W
Reactive power Q, V·Ar
R
80 @ 0°
4 @ 180°
320
0
L
105.8 @ 10.9°
10.58 @ 100.9°
0
1119.4
C
52.9 @ 169.1°
10.58 @ 79.1°
0
-559.7
V
60 @ 30°
10.58 @ -100.9°
415.6
-479.8
I
185 @ 6.2°
4 @ 0°
-735.6
-79.9
0
0
Video
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