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E245 Homework 1 : DC Circuits Solutions Instructions Print your name clearly. If not readable, it may be impossible to assign a grade to your work. Show solutions neatly and show all steps in solving the problem. If solutions are not readable, a grade can not be assigned. If all steps in solving a problem are not shown, partial credit can not be assigned. You may find the notes at the end of the set of problems helpful. A. Problems to be solved Problem 1: For the circuit in Figure 1 below, determine the equivalent resistance (illustrated in Figure 1b) between output points A and B by combining resistors in parallel and combining resistors in series in the starting circuit of Figure 1a. Show all steps in your reduction to a single equivalent resistance (e.g., what resistors are combined and the value when combined for each step along the way to the final answer). You may find it useful to redraw the circuit as you proceed through the combining of resistors. SOLUTION: R5 and R7 are in parallel. RA = (R5 * R7)/(R5 + R7) = (3 * 6)/(3 + 6) = 2 ohms R4 and RA are in series RB = R4 + RA = 1 + 2 = 3 ohms R6 and RB are in parallel RC = (R6 * RB)/(R6 + RB) = (6 * 3)/(6 + 3) = 2 ohms R2, RC, and R3 are in series RD = R2 + RC + R3 = 3 + 2 + 1 = 6 ohms R1 and RD are in parallel Req = (R1 * RD)/(R1 + RD) = (3 * 6)/(3 + 6) = 2 ohms RETURN THIS FRONT PAGE AS PAGE ONE OF YOUR SOLUTIONS
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R2 R1 R3 R5 R6 A B R7 R4 R1 = 3 ohms R2 = 3 ohms R3 = 1 ohm R4 = 1 ohm R5 = 3 ohms R6 = 6 ohms R7 = 6 ohms A B R eq Equivalent Resistance (a) (b) Figure 1 Problem 2: Figure 2a is similar to Figure 1a but replaces R6 with a current source I A = 2 amps and adds a voltage source V A = 3 Volts in the loop containing R7. Again, you are to determine the equivalent resistance between points A and B. To do this, you need to replace the current and voltage sources by their equivalent resistances. Answer the following questions. What is the resistance of a current source?
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