SeriesParallel DC Circuits
DC Electric Circuits
Don’t just sit there! Build something!! 
Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.
You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the änswers” instead of a book or another person. For successful circuitbuilding exercises, follow these steps:
 1.
 Carefully measure and record all component values prior to circuit construction.
 2.
 Draw the schematic diagram for the circuit to be analyzed.
 3.
 Carefully build this circuit on a breadboard or other convenient medium.
 4.
 Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements onebyone on the diagram.
 5.
 Mathematically analyze the circuit, solving for all values of voltage, current, etc.
 6.
 Carefully measure those quantities, to verify the accuracy of your analysis.
 7.
 If there are any substantial errors (greater than a few percent), carefully check your circuit’s construction against the diagram, then carefully recalculate the values and remeasure.
Avoid very high and very low resistor values, to avoid measurement errors caused by meter “loading”. I recommend resistors between 1 kΩ and 100 kΩ, unless, of course, the purpose of the circuit is to illustrate the effects of meter loading!
One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another timesaving technique is to reuse the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.
In a series circuit, certain general rules may be stated with regard to quantities of voltage, current, resistance, and power. Express these rules, using your own words:
Ïn a series circuit, voltage . . .”
Ïn a series circuit, current . . .”
Ïn a series circuit, resistance . . .”
Ïn a series circuit, power . . .”
For each of these rules, explain why it is true.
In a parallel circuit, certain general rules may be stated with regard to quantities of voltage, current, resistance, and power. Express these rules, using your own words:
Ïn a parallel circuit, voltage . . .”
Ïn a parallel circuit, current . . .”
Ïn a parallel circuit, resistance . . .”
Ïn a parallel circuit, power . . .”
For each of these rules, explain why it is true.
Identify which of these components are connected directly in series with each other, and which are connected directly in parallel with each other:

Assume that the open wire ends are connection points to a power source. In circuits where ground symbols appear, consider ground as the other side of the power source.
In this seriesparallel circuit, resistors R1 and R2 are in series with each other, but resistor R3 is neither in series nor in parallel with either R1 or R2:

Normally, the first step in mathematically analyzing a circuit such as this is to determine the total circuit resistance. In other words, we need to calculate how much resistance the voltage source ßees” in the network formed by R1, R2, and R3. If the circuit were a simple series configuration, our task would be easy:

Likewise, if the circuit were a simple parallel configuration, we would have no difficulty at all calculating total resistance:

Due to the fact that our given circuit is neither purely series nor purely parallel, though, calculation of total resistance is not a simple onestep operation. However, there is a way we could simplify the circuit to something that is either simple series or simple parallel. Describe how that might be done, and demonstrate using numerical values for resistors R1, R2, and R3.
Determine the amount of electrical resistance indicated by an ohmmeter connected between the following points in this circuit:

 •
 Between points A and B =
 •
 Between points A and C =
 •
 Between points C and D =
 •
 Between points D and B =
 •
 Between points B and C =
Explain whether or not it makes any sense to speak of a “total” resistance for this network.
Antique American automobiles often used 6 volt electrical systems instead of the 12 volt components found in more modern cars and trucks. People who restore these old vehicles may have difficulty finding old 6volt generators and batteries to replace the defective, original units. An easy solution is to update the vehicle’s generator and battery with modern (12 volt) components, but then another problem arises.
A 12 volt generator and 12 volt battery will overpower the old 6 volt headlights, brake lights, and other electrical “loads” in the vehicle. A solution used by antique automobile restorers is to connect resistors between the 12volt generator system and the 6volt loads, like this:

Explain why this solution works, and also discuss some of the disadvantages of using resistors to adapt the new (12 volt) to the old (6 volt) components.
A student built this resistor circuit on a solderless breadboard, but made a mistake positioning resistor R3. It should be located one hole to the left instead of where it is right now:

Determine what the voltage drop will be across each resistor, in this faulty configuration, assuming that the battery outputs 9 volts.
 •
 R_{1} = 2 k Ω V_{R1} =
 •
 R_{2} = 1 k Ω V_{R2} =
 •
 R_{3} = 3.3 k Ω V_{R3} =
 •
 R_{4} = 4.7 k Ω V_{R4} =
 •
 R_{5} = 4.7 k Ω V_{R5} =
Suppose you were designing a circuit that required two LEDs for “power on” indication. The power supply voltage is 15 volts, and each LED is rated at 1.6 volts and 20 mA. Calculate the dropping resistor sizes and power ratings:

After doing this, a coworker looks at your circuit and suggests a modification. Why not use a single dropping resistor for both LEDs, economizing the number of components necessary?

Recalculate the dropping resistor ratings (resistance and power) for the new design.
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