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Series DC circuits
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Questions
Question 1
Identify which of these circuits is a series circuit (there may be more than one shown!):
A B
C
D
E
F
file 01717
Question 2
Most flashlights use multiple 1.5 volt batteries to power a light bulb with a voltage rating of several volts. Draw a schematic diagram of showing how multiple batteries may be connected to achieve a total voltage greater than any one of the batteriesā individual voltages. file 00038
How much voltage does the light bulb receive in this circuit? Explain your answer.
3 volts 24 volts 6 volts
Also, identify the polarity of the voltage across the light bulb (mark with ā+ā and ā-ā signs). file 01720
Question 6
Re-draw this circuit in the form of a schematic diagram:
file 00068
Suppose I connect two resistors in series with one another, like this:
3.3 kĪ© 3.3 kĪ©
Resistor leads joined
by twisting together
How much electrical resistance would you expect an ohmmeter to indicate if it were connected across the combination of these two series-connected resistors?
3.3 kĪ© 3.3 kĪ©
Resistor leads joined
by twisting together
A COM
V
V A
A
OFF
Explain the reasoning behind your answer, and try to formulate a generalization for all combinations of series resistances. file 01721
In this circuit, three resistors receive the same amount of current (4 amps) from a single source. Calculate the amount of voltage ādroppedā by each resistor, as well as the amount of power dissipated by each resistor:
24 volts
file 00090
Question 11
Explain, step by step, how to calculate the amount of current (I) that will go through each resistor in this series circuit, and also the voltage (V ) dropped by each resistor:
R1 R2 R
1k5 10k 4k
36 V
file 01549
The brightness of a light bulb ā or the power dissipated by any electrical load, for that matter ā may be varied by inserting a variable resistance in the circuit, like this:
Variable resistance
This method of electrical power control is not without its disadvantages, though. Consider an example where the circuit current is 5 amps, the variable resistance is 2 Ī©, and the lamp drops 20 volts of voltage across its terminals. Calculate the power dissipated by the lamp, the power dissipated by the variable resistance, and the total power provided by the voltage source. Then, explain why this method of power control is not ideal. file 00104
Light-emitting diodes, or LEDs, are rugged and highly efficient sources of light. They are far more rugged and efficient than incandescent lamps, and they also have the ability to switch on and off much faster because there is no filament inside needing to heat or cool:
Close-up view of a
light-emitting diode
LEDs are low voltage devices, typically rated in the range of 1.5 to 2 volts DC maximum. Single diodes generally draw low currents as well, about 20 milliamps each. The problem is, how do you operate an LED from a typical electronic power source, which may output 24 volts DC or more?
Power
supply
LED
The LED will become damaged
if overpowered!
The answer is to use a series dropping resistor:
Power
supply
LED
Dropping resistor
Calculate the necessary resistance value and minimum power rating of a series dropping resistor for an LED rated at 1.7 volts and 20 mA, and a power supply voltage of 24 volts. file 01776
Calculate the necessary series ādroppingā resistor value to operate a 1.6 volt, 20 mA LED from a 15 volt DC power source. Also, calculate the power dissipated by the resistor while operating.
R = PR =
file 02304
Question 16
Calculate the necessary series ādroppingā resistor value to operate a 1.8 volt, 20 mA LED from a 34 volt DC power source. Also, calculate the power dissipated by the resistor while operating.
R = PR =
file 02305
Question 17
The formula for calculating total resistance of three series-connected resistors is as follows:
R = R 1 + R 2 + R 3
Algebraically manipulate this equation to solve for one of the series resistances (R 1 ) in terms of the other two series resistances (R 2 and R 3 ) and the total resistance (R). In other words, write a formula that solves for R 1 in terms of all the other variables. file 03066
Question 18
Suppose that an electric heater, which is nothing more than a large resistor, dissipates 500 watts of power when directly connected to a 110 volt source:
110 V 500 W
Now suppose that exact same heater is connected to one end of a long two-wire cable, which is then connected to the same 110 volt source. Assuming that each conductor within the cable has an end-to-end resistance of 3 ohms, how much power will the heater dissipate?
110 V
P = ???
file 03252
Complete the table of values for this circuit:
V
I
R
P
R 1
R 2
R 3
R 1 R 2 R 3 Total
14 V
780 Ī© 1.5 kĪ© 3.3 kĪ©
1.5 kĪ©
3.3 kĪ©
file 01957
Question 22
Complete the table of values for this circuit:
1 kĪ©
6 volts 9 volts
2.2 kĪ©
6.8 kĪ©
V
I
R
P
R 1
R 2 R 3
R 4
R 1 R 2 R 3 R 4 Total
1 kĪ© 2.2 kĪ© 6.8 kĪ© 470 Ī©
file 01722
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:
āIn a series circuit, voltage.. .ā
āIn a series circuit, current.. .ā
āIn a series circuit, resistance.. .ā
āIn a series circuit, power.. .ā
For each of these rules, explain why it is true. file 00291
Question 24
Predict how all test point voltages (measured between each test point and ground) in this circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):
TP1 TP
TP
R 1
R 2
R 3
V 1
- Resistor R 1 fails open:
- Resistor R 2 fails open:
- Resistor R 3 fails open:
- Solder bridge (short) past resistor R 2 : For each of these conditions, explain why the resulting effects will occur. file 03709
After this, the student measures between terminals 1 and 2 (across resistor R 1 ), and gets a reading of 0 volts. Complete the table based on this last piece of data:
Measurement taken Battery Wire +/1 R 1 Wire 2/3 R 2 Wire 4/- VR 2 = 0 V O O O O S O V 1 ā 4 = 6 V OK OK O O S OK VR 1 = 0 V
file 03585
Question 26
This voltage divider circuit has a problem: there is no voltage output between terminals 7 and 8.
1 2 3 4
6 V R 2
R 3
R 4
5 6 7 8
R 1
A technician has taken several measurements with a voltmeter, documenting them chronologically from top to bottom in the far-left column:
Measurement Batt (+)/1 R 1 2/3 R 2 4/5 R 3 6/7 R 4 8/(-) V 1 ā 8 = 6 V V 1 ā 5 = 0 V V 5 ā 7 = 6 V
Fill in all cells of this table with one of three different symbols, representing the status of each component or wire (numbers separated by a slash indicate the wire connecting those terminals):
- O for an āopenā fault
- S for an āshortā fault
- OK for no fault You are to assume that there is only one fault in this circuit, and that it is either a complete break (open) or a direct short (zero resistance). After completing the table, assess whether or not the exact fault may be known from the data recorded thus far. If not, suggest the next logical voltage measurement to take. file 03586
Donāt 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 āanswersā instead of a book or another person. For successful circuit-building exercises, follow these steps:
- Carefully measure and record all component values prior to circuit construction.
- Draw the schematic diagram for the circuit to be analyzed.
- Carefully build this circuit on a breadboard or other convenient medium.
- Check the accuracy of the circuitās construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.
- Mathematically analyze the circuit, solving for all values of voltage, current, etc.
- Carefully measure those quantities, to verify the accuracy of your analysis.
- If there are any substantial errors (greater than a few percent), carefully check your circuitās construction against the diagram, then carefully re-calculate the values and re-measure. Avoid very high and very low resistor values, to avoid measurement errors caused by meter āloadingā. I recommend resistors between 1 kĪ© and 100 kĪ©, 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 time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you wonāt have to measure any componentās value more than once. file 00405
Answer 4
3 volts 6 volts 4.5 volts
7.5 volts
Follow-up question: draw the direction of current in this circuit.
Answer 5
3 volts 24 volts 6 volts
15 volts
Follow-up question: being that 30 volts is the commonly accepted ādangerā threshold voltage for electric shock, determine whether or not this particular circuit poses a shock hazard.
Answer 6
Answer 7
3.3 kĪ© 3.3 kĪ©
Resistor leads joined
by twisting together
A COM
V
V A
A
OFF
kĪ©
Follow-up question: how much resistance would you expect the ohmmeter to register if there were three similarly-sized resistors connected in series instead of two? What if there were four resistors?
Answer 8
The three light bulbs would glow dimly.
Answer 9
The current through each of the lights bulbs is guaranteed to be equal. The voltage across each of the light bulbs, in this particular case (with identical bulbs), happens to be equal.
Answer 10
E1Ī© = 4 volts E2Ī© = 8 volts E3Ī© = 12 volts
P1Ī© = 16 watts P2Ī© = 32 watts P3Ī© = 48 watts
Follow-up question: Compare the direction of current through all components in this circuit with the polarities of their respective voltage drops. What do you notice about the relationship between current direction and voltage polarity for the battery, versus for all the resistors? How does this relate to the identification of these components as either sources or loads?
