EE001A Engineering Circuit Analysis Assignment
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EE001A Engineering Circuit Analysis Assignment
EE001A Engineering Circuit Analysis I Department of Electrical Engineering University of California – Riverside
Instructor: Roman Chomko
Homework 4 EE 001A
Spring 2014
Homework* 4
Basic Resistor Networks, Node Voltage and Loop Current Methods
Due Date: Thursday, May 8, 2014
* Collaboration is allowed
ee001a hw 4
2
Problem #1 (Equivalent Resistance of Resistor Networks)
Using a generic method shown in Flowchart 1 of Lecture 9 (STEPS 1 through 3) determine the equivalent resistance of a resistor network shown schematically in Figure P1.
Figure P1 Resistor Network
Note: DO NOT perform STEP 4 of the procedure
Problem #2 (Resistor Network Analysis by Ladder Method)
Background
The Ladder Method discussed in Lecture 9 is naturally applied for analysis of signal filters (both Low-Pass and High-Pass). While a complete analysis of these types of problems is beyond the scope of EE1A, the method itself is unchanged and can be directly demonstrated on a simple two ladder rung resistor network circuit shown in Figure P2 (that looks like a ladder, that’s why the name).
Statement
Solve a circuit in Figure P2 by Ladder Method.
R4vS
Figure P2 Resistor network
ee001a hw 4
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Problem #3 (Node Voltage Method, or Nodal Analysis, Alexander 3.2)
Figure P3
Solve the circuit of Figure P3 by Node Voltage Method (NVM).
Note: do not simplify any resistor networks.
Hints:
1) join all redundant nodes at a single node and denote its node voltage as shown;
2) start solving the problem as though you are solving it with NBM (assign all reference voltages and currents using the passive sign convention for convenience in properly writing the Ohm’s Law for resistors);
3) write KCL’s for (N-1) non-redundant nodes;
4) express all voltages in terms of node voltages (remember: V= v+ – v-);
5) using the Ohm’s Law express all currents in terms of voltages, and than in terms of node voltages using 4);
6) solve the resulting system of equations in 3) by whichever method you like (calculators is fine);
7) find all currents and voltages based on node voltages in 4) and 5).
Problem #4 (Node Voltage Method, or Nodal Analysis, Alexander 3.12)
Figure P4
ee001a hw 4
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Solve the circuit of Figure P4 for V0 by Node Voltage Method (NVM).
Hints:
1) see Problem 3 hints;
2) you will need an extra equation when done with KCL equations – it will come from the constraint equation for VS: express VS in terms of corresponding node voltages (remember Problem 3, Hint 4).
Problem #5 (Loop Current Method, or Mesh Analysis)
Figure P5 Wheatstone Bridge Circuit
- Solve a bridge circuit shown in Figure P5 by Loop Current Method (LCM)
- Compute the equivalent resistance of this bridge resistor network using
Hints:
1) start solving the problem as though you are solving it with NBM (assign all reference voltages and currents using the passive sign convention for convenience in properly writing the Ohm’s Law for resistors);
2) assign KVL loops, write KVL’s for N independent loops;
3) assume that KVL loops correspond to loop currents;
4) express all currents in terms of loop currents (remember: each branch current is expressed as a sum of loop currents that touch this branch, and if a loop current flows opposite to the branch current take it with a negative sign);
5) using the Ohm’s Law express all voltages in terms of (branch) currents, and than in terms of loop currents using 4);
ee001a hw 4
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6) solve the resulting system of equations in 3) by whichever method you like (calculators is fine);
7) find all currents and voltages based on loop currents in 4) and 5).
Problem #6 (Loop Current Method, or Mesh Analysis)
Figure P6
Solve the circuit of Figure P6 (same as in Problem 4) for V0 by Loop Current Method (LCM).
Hints: after writing KVL equations you will need an extra equation to solve the system – express ID in terms of the corresponding loop currents to obtain a required constraint equation.
Design Problem #7† (Wheatstone Bridge Sensor)
In Lecture 12 in Design Circuit 1 we found the nominal resistance R5 visually by numerically varying it and testing for the condition ig = 0 (that is, when no current is flowing through the gauge). We can also find it exactly using the analytic results obtained for the bridge circuit in Example 3.
Find R5 (nominal)
exactly.
† Optional. Extra credit will be given for a complete solution.
RUBRIC
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POOR / UNSATISFACTORY |
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EXCELLENT |
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