(a) Formulate node-voltage equations for the bridge circuit in Figure \(\mathrm{P}_{3}-8\).

(b) Solve for \(v_{\mathrm{x}}\) and \(i_{\mathrm{x}}\) when \(R_{1}=R_{4}=1 \mathrm{k} \Omega, R_{2}=R_{3}=\) \(1.5 \mathrm{k} \Omega, R_{\mathrm{X}}=680 \Omega\), and \(v_{\mathrm{S}}=12 \mathrm{~V}\).
(c) Repeat (b) when \(R_{4}\) is a variable resistor that varies from \(10 \Omega\) to \(100 \mathrm{k} \Omega\). At what value of \(R_{4}\) is the voltage across \(R_{\mathrm{x}}=\mathrm{o}\) V? Use Multisim to find the value by either varying \(R_{4}\) 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, \(1.5 \mathrm{k} \Omega\). Under "Points to sweep", choose "Decade" sweep variation type. "Start" at \(10 \Omega\); "Stop" at \(100 \mathrm{k} \Omega\). Use 100 points per decade - 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 \(680-\Omega\) resistor, create an expression for it, such as \(V(2)-V(3)\) if those are the node names of the two nodes determining the resistor

voltage. Choose "Run." Grapher View will plot a graph of the resistance value versus the voltage across the \(680-\Omega\) 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.
(d) Repeat the sweep changing \(R_{\mathrm{x}}\) from \(680 \Omega\) to \(1 \Omega, 100\) \(\Omega, 10 \mathrm{k} \Omega, 1 \mathrm{M} \Omega\), and \(1 \mathrm{G} \Omega\). What value of \(R_{4}\) makes \(v_{\mathrm{x}}\) go to zero in each case? What is the range of \(v_{\mathrm{x}}\) in each case?
What conclusions can you reach?

Transcribed Image Text:

1 + VS R ww R3 Rx ww +Vx w R W R