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Series-Parallel DC Circuits
41 questions By Tony R. Kuphaldt
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Question 22 of 41
Think of a way to re-wire the electrical system of this old automobile (with 6-volt light bulbs) so as to not require resistors between the loads and the generator/battery portion of the circuit (operating at 12 volts each).
Reveal answerConnect the light bulb pairs in series instead of parallel. This way, each light bulb will receive 6 volts, with a total system voltage of 12 volts.
Follow-up question: there is a disadvantage of this strategy, though, and it concerns the safety of operating the automobile. Explain what this disadvantage is.
Notes:This solution works only because the load sets are in pairs, and because 6 6 = 12. One benefit of this solution is greater efficiency, as there are no resistors in the circuit to “waste” power by dissipating it in the form of heat. However, there is a disadvantage to doing things this way, as indicated by the follow-up question. Discuss this disadvantage with your students, reinforcing the idea that the most efficient engineering solutions may not be the best when assessed from other perspectives, such as safety!
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Question 23 of 41
Calculate the voltage drops VAB, VBC, and VCD in the following circuit:
Reveal answerVAB = 461 mV
VBC = 0 V
VCD = 1.039 V
Follow-up question: explain why the voltage between points A and B (VAB) would increase if the 1200 Ω resistor were to fail shorted. Hint: imagine a “jumper” wire connected across that resistor to simulate a shorted failure.
Challenge question: explain how you can calculate these same answers without ever having to calculate total circuit current.
Notes:Ask your students how they could tell VBC must be zero, just by examining the circuit (without doing any math). If some students experience difficulty answering this question on their own, have them translate the drawing into a proper schematic diagram.
Students often have difficulty formulating a method of solution: determining what steps to take to get from the given conditions to a final answer. While it is helpful at first for you (the instructor) to show them, it is bad for you to show them too often, lest they stop thinking for themselves and merely follow your lead. A teaching technique I have found very helpful is to have students come up to the board (alone or in teams) in front of class to write their problem-solving strategies for all the others to see. They don’t have to actually do the math, but rather outline the steps they would take, in the order they would take them.
By having students outline their problem-solving strategies, everyone gets an opportunity to see multiple methods of solution, and you (the instructor) get to see how (and if!) your students are thinking. An especially good point to emphasize in these “open thinking” activities is how to check your work to see if any mistakes were made.
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Question 24 of 41
Calculate the voltage magnitude and polarity between points A and D in this circuit, assuming a power supply output voltage of 10.5 volts:
Also, calculate the total current output by the power supply as it energizes this resistor network.
Reveal answerVAD = 7.31 volts, A positive and D negative. The total power supply current is 4.36 mA.
Follow-up question: explain why the voltage across the 4.7 kΩ resistor would go to zero if the 1.5 kΩ resistor were to fail open.
Notes:Though some students might not realize it at first, there is no series-parallel analysis necessary to obtain the voltage drop VAD.
Students often have difficulty formulating a method of solution: determining what steps to take to get from the given conditions to a final answer. While it is helpful at first for you (the instructor) to show them, it is bad for you to show them too often, lest they stop thinking for themselves and merely follow your lead. A teaching technique I have found very helpful is to have students come up to the board (alone or in teams) in front of class to write their problem-solving strategies for all the others to see. They don’t have to actually do the math, but rather outline the steps they would take, in the order they would take them.
By having students outline their problem-solving strategies, everyone gets an opportunity to see multiple methods of solution, and you (the instructor) get to see how (and if!) your students are thinking. An especially good point to emphasize in these “open thinking” activities is how to check your work to see if any mistakes were made.
As a follow-up to the follow-up question, ask your students what other resistor in this circuit would completely lose voltage given an open failure of the 1.5 kΩ resistor.
How did you guys find the answer for Q5, figure 6