Formulate node-voltage equations for the bridge circuit in

Question

(a) Formulate node-voltage equations for the bridge circuit in Figure.

(b) Solve for vx and ix when R₁ = R₄ =1kΩ, R₂ = R₃ = 1:5 kΩ, Rx = 680 Ω, and v_S = 12 V.

(c) Repeat (b) when R₄ is a variable resistor that varies from 10 Ω to 10 kΩ. At what value of R₄ is the voltage across R_x = 0 V? Use Multisim to find the value by either varying R4 by trial and error to approach the answer, or using a "Parameter sweep" found under Analyses.

To use the latter, proceed as follows: Under "Parameter sweep" select "Device type:" Resistor; "Name:" your name for our R₄; "Parameter (what you wish to vary):" resistance; "Present value:" Any value within your range-say, 1 kΩ. Under "Points to sweep," choose "Linear" sweep variation type. "Start" at 10 Ω; "Stop" at 10 kΩ. Use 100 points-Multisim automatically calculates the increment. Under "More Options" choose "DC Operating Point." Then go to the output tab under the Parameter Sweep window.

Since you want the voltage across the 680-Ω resistor, create an expression for it, such as V (2)-V (3) if those are the node names of the two nodes determining the voltage. Choose "Simulate." Grapher View will plot a graph of the resistance value versus the voltage across the 680-Ω resistor. Make sure the grid lines are shown on your graph. Use the cursor to find the value of resistance that causes the voltage to go to zero.