Homework 7 Due Friday September 9 1 For 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 V1 in terms of R and Vs1 if Vs2 3 Vs1 Figure 1 Model circuits for Problem 1 2 The purpose of this problem is to write the nodal equations directly by inspection of the circuit diagram of Figure 2 Recall that when the network has only independent current sources and resistors the nodal equation matrix is symmetric and the entries can be written down by inspection as per discussion following the textbook Example 3 2 Construct the nodal equations in matrix form for the circuit of Figure 2 by inspection 3 Wednesday September 7 2011 The circuit of Figure 3 is an experimental measurement circuit for determining temperature inside a cavern underneath the Polar ice cap The cavern is heated by 1 Figure 2 Model circuit for Problem 2 a fissure leading to some volcanic activity deep in the earth The resistor Rsensor changes its value linearly from 30 k to 130 k as a function of temperature over the range 25 C to 25 C The nominal temperature of the cavern is 0 C In this type of circuit the voltage VC VB is a measure of how the temperature changes Suppose that Vs 50 V and in k R1 40 R2 88 R3 40 and R4 25 Note that the 88 k resistor is a result of manufacturing tolerances that often permit deviations from a nominal of say 90 k by as much as 20 As usual it is cost versus precision a Write a set of nodal equations in the variables VB and VC b Assuming Rsensor 80 k at 0 C put the nodal equations in matrix form and solve for the node voltages VB and VC c Determine the power delivered by the source day September 7 2011 Figure 3 Model circuit for Problem 3 2
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