Problem #7 R, = 42 R, = 3 2 R, = 7 N A B V, = 12V R, = 2 2 R, = 5 2 Vz = 6 V G Assume all given values are known to three (3) significant figures. Express voltage in volts (V) current in amperes (A), and power in watts (W). Questions Utilize the node-voltage method for your solution. For consistency, let I1, I2, I3, I4, and Iş be the branch currents through resistors R1, R2, R3, R4, and Rs respectively. a) Re-draw the schematic with arrows to show the branch currents that are either entering or leaving nodes A and B. Include the new drawing in your document. Note: It is your choice which direction you want to point the arrows. Once you have decide be consistent when writing the circuit equations. b) Write the KCL equations at node A and at node B in terms of the branch currents I thru Is. c) Expand the KCL equations in terms of the unknown voltages Va and V8 and express your f set of simultaneous equations in matrix-vector format (i.e., Mx = b, where M is the matrix linear coefficients, x is the vector of unknown variables, and b is the vector of constants). d) Calculate the nodal voltages V, and Vg (i.e., the voltages at nodes A and B w.r.t. ground) e) Calculate the value of the current through resistor R1. f) Calculate the value of the current through resistor R2. g) Calculate the value of the current through resistor R3. h) Calculate the value of the current through resistor R4. i) Calculate the value of the current through resistor Rs. j) In what direction is the branch current actually flowing through R3 (toward node A or away from A)? Justify your answer.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.52P

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Problem #7
R, = 4 N
A
R, = 3 N
в
R3 = 72
V, = 12V
R, = 2 N
R_ = 52
V2 = 6 V
G
Assume all given values are known to three (3) significant figures. Express voltage in volts (V),
current in amperes (A), and power in watts (W).
Questions
Utilize the node-voltage method for your solution. For consistency, let I1, I2, I3, I4, and Iş be the
branch currents through resistors R1, R2, R3, R4, and Rs respectively.
a) Re-draw the schematic with arrows to show the branch currents that are either entering or
leaving nodes A and B. Include the new drawing in your document.
Note: It is your choice which direction you want to point the arrows. Once you have decided,
be consistent when writing the circuit equations.
b) Write the KCL equations at node A and at node B in terms of the branch currents I thru Is.
c) Expand the KCL equations in terms of the unknown voltages VA and Vg and express your final
set of simultaneous equations in matrix-vector format (i.e., Mx = b, where M is the matrix of
linear coefficients, x is the vector of unknown variables, and b is the vector of constants).
d) Calculate the nodal voltages V¼ and V8 (i.e., the voltages at nodes A and B w.r.t. ground)
e) Calculate the value of the current through resistor R1.
f) Calculate the value of the current through resistor R2.
g) Calculate the value of the current through resistor R3.
h) Calculate the value of the current through resistor R4.
i) Calculate the value of the current through resistor Rs.
j) In what direction is the branch current actually flowing through R3 (toward node A or away
from A)? Justify your answer.

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