Download Problem 3.6

Problem 3.6 Part A Find the equivalent resistance with respect to the terminals a and b in the following circuit. Express your answer to two significant figures and include appropriate units. Solution: The equivalent resistance is: {[(20 Ohms || 60 Ohms) + (12 Ohms || 24 Ohms) + 7 Ohms] || 120 Ohms} + 15 Ohms + 25 Ohms = {[15 + 8 + 7] || 120} + 15 + 25 = 64 Ohms Part B Find the equivalent resistance with respect to the terminals a and b in the following circuit. Express your answer to two significant figures and include appropriate units. Solution: The equivalent resistance is: The resistance on the outer (rightmost) segment is: [(35 + 40) || 50] + 20 = 50 ohms The 50 ohms is then in parallel with the 75 ohms = 30 ohms The 30 ohms is then in series with the 10 ohm resistor = 40 ohms The 40 ohms is then in parallel with the 60 ohm resistor = 24 ohms The 18 ohms and 9 ohm resistors are in parallel = 6 ohms This 6 ohm is then in series with the 24 ohms = 30 ohms The 30 ohms is then in parallel with 30 ohms = 15 ohms Finally, the 15 ohms is in series with the 10 ohm and 5 ohm resistors = 30 ohms Part B Find the equivalent resistance with respect to the terminals a and b in the following circuit. Express your answer to two significant figures and include appropriate units. Solution: The equivalent resistance is: On the left side: (50 + 30) || 20 = 16 Ohms On the right side: (30 + 24) || 27 = 18 ohms The 16 ohms on the left side is then in series with 14 Ohms = 30 ohms The 18 ohms on the right side is then in series with 12 ohms = 30 ohms That leaves the two 30 ohm resistors in parallel = 15 ohms And finally, the 15 ohms is in series with the 3 ohms and 2 ohms = 20 ohms.