Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 05 (c)
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Question Section 201 05 (c) 

Consider the following graph, interpreted as a resistor network with all resistances R = 1. (c) Suppose that by attaching a battery, the voltage at vertex 1 is held at b_{1} and the voltage at vertex 2 is held at b_{2}. Write down vectors v and J so that the equation Lv = J describes this situation. Explain what each entry of v and J represents, and how you can use the entries to compute the effective resistance between vertices 1 and 2. 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 201 05 (c)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Here every entry is the voltage at the corresponding node. b_{1} and b_{2} are the voltages held by the battery connected at nodes 1 and 2. Here every entry is the current flowing into/out of the corresponding node. c is the current coming out of node 1 from the battery, c is the current coming out of node 2 from the battery. To find R_{eff} remember Ohm's law: V=IR. Hence Notice that c is determined by the resistance of the rest of the circuit. If c is unknown, the effective resistance can be computed using Schur’s Complement. Remember: 