VM117

VM117
Electric Current Flowing in a Network

Overview

Reference:

A. E. Fitzgerald, D. E. Higginbotham, Basic Electrical Engineering, 2nd Edition, McGraw-Hill Book Co., Inc., New York, NY, 1957, pg. 22, ex. 1-11.

Analysis Type(s):

Thermal (electrical) Analysis (ANTYPE = 0)

Element Type(s):

Coupled Thermal-Electric Line Elements (LINK68)

Electric Circuit Element (CIRCU124)

Input Listing:

vm117.dat

Test Case

The network shown below is that of an unbalanced bridge used in measuring resistance. With the circuit parameters as specified, determine the current I_a-b flowing in each branch (from a to b) and the voltage at each node.

Figure 167: Electric Current Problem Sketch

Material Properties

R_2-1 = 20 Ω

R_3-1 = 10 Ω

R_2-3 = 9 Ω

R_4-2 = 30 Ω

R_4-3 = 90 Ω

V_o = 100 volts

Analysis Assumptions and Modeling Notes

The branch resistance is implicitly input as the element area (real constant). A convenient geometric configuration is assumed ( = 1 ft) and the material resistivity is taken as 1 ohm-ft (input as material property RSVX). The areas are calculated from the relation: A = ρ /R, where A = area of element (ft²), = length of element (ft), ρ = resistivity (ohm-ft), R = given resistance (ohm).

Node 1 is assumed to be the ground node for reference. POST1 is used to extract the currents in each branch. A negative value indicates that current flow is opposite to the assumed direction (Node I to J of the element).

Results Comparison

LINK68	Target	Mechanical APDL	Ratio
V₁, volts	0.0	0.0	-
V₂, volts	28.0	28.0	1.00
V₃, volts	19.0	19.0	1.00
V₄, volts	100.0	100.0	1.00
I_2-1, amps	1.4	1.4	1.00
I_3-1, amps	1.9	1.9	1.00
I_2-3, amps	1.0	1.0	1.00
I_4-2, amps	2.4	2.4	1.00
I_4-3, amps	0.9	0.9	1.00
I_1-4, amps	3.3	3.3	1.00

CIRCU124	Target	Mechanical APDL	Ratio
V₁, volts	0.0	0.0	-
V₂, volts	28.0	28.0	1.00
V₃, volts	19.0	19.0	1.00
V₄, volts	100.0	100.0	1.00
I_2-1, amps	1.4	1.4	1.00
I_3-1, amps	1.9	1.9	1.00
I_2-3, amps	1.0	1.0	1.00
I_4-2, amps	2.4	2.4	1.00
I_4-3, amps	0.9	0.9	1.00
I_1-4, amps	3.3	3.3	1.00