Homework 7Due: Friday, September 91For the circuit of Figure 1, write a single node equation in G1, G2, G3, Vs1, and Vs2.For a fixed R > 0, R1= R, R2= 1.5 R, R3= 3 R. Compute V1in terms of R andVs1if Vs2= 3 Vs1Wednesday, September 7, 2011Figure 1: Model circuits for Problem 1.2The purpose of this problem is to write the nodal equations directly by inspection ofthe circuit diagram of Figure 2. Recall that when the network has only independentcurrent sources and resistors, the nodal equation matrix is symmetric and the entriescan be written down by inspection as per discussion following the textbook Example3.2. Construct the nodal equations in matrix form for the circuit of Figure 2 byinspection.3The circuit of Figure 3 is an experimental measurement circuit for determining tem-perature inside a cavern underneath the Polar ice cap. The cavern is heated by1Wednesday, September 7, 2011Figure 2: Model circuit for Problem 2a fissure leading to some volcanic activity deep in the earth. The resistor Rsensorchanges its value linearly from 30 kΩ to 130 kΩ as a function of temperature overthe range − 25◦C to + 25◦C. The nominal temperature of the cavern is 0◦C. In thistype of circuit, the voltage VC− VBis a measure of how the temperature changes.Suppose that Vs= 50 V, and in kΩ, R1= 40, R2= 88, R3= 40 and R4= 25. Notethat the 88 kΩ resistor is a result of manufacturing tolerances that often permitdeviations from a nominal of, say, 90 kΩ, by as much as 20%. As usual, it is costversus precision.(a) Write a set of nodal equations in the variables VBand VC.(b) Assuming Rsensor= 80 kΩ at 0◦C, put the nodal equations in matrix formand solve for the node voltages, VBand VC.(c) Determine the power delivered by the source.Figure 3: Model circuit for Problem
View Full Document