Practice: Series-Parallel Circuits

Question 1

Identify which of these components are connected directly in series with each other, and which are connected directly in parallel with each other:

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Question 2

Determine which light bulb(s) will glow brightly, and which light bulb(s) will glow dimly (assuming all light bulbs are identical).

Additional Discussion

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Question 3

Complete the table of values for this circuit:

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Question 4

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.

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Question 5

Imagine you are using a digital voltmeter to measure voltages between pairs of points in a circuit, following the sequence of steps shown in the following diagrams:

How much voltage would be registered by the voltmeter in each of the steps? Be sure to include the sign of the DC voltage measured (note the coloring of the voltmeter leads, with the red lead always on the first point denoted in the subscript: \(V_{BA}\) = red lead on "B" and black lead on "A"):

What is the algebraic sum of these voltages?

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Question 6

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.

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Question 7

Calculate the power supply’s output (total) current:

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Question 8

Complete the table of values for this circuit:

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Question 9

Calculate both the total resistance of this voltage divider circuit (as "seen" from the perspective of the 25 volt source) and its output voltage (as measured from the \(V_{out}\) terminal to ground):

Note that the upper 5 k\(\Omega\) potentiometer is set to its 20/ position (\(m = 0.2\)), while the lower 5 k\(\Omega\) potentiometer is set to its 90/ position (\(m = 0.9\)), and the 100 k\(\Omega\) potentiometer is set to its 40/ position (\(m = 0.4\)).

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Question 10

Determine the voltages (with respect to ground) at points A and B in this circuit under four different conditions: both loads off, load 1 on (only), load 2 on (only), and both loads on:

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Question 11

What will happen to each resistor’s voltage in this circuit if resistor R4 fails shorted? Provide individual answers for each resistor, please.

Also, comment on the practical likelihood of a resistor failing shorted, as opposed to failing open.

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Question 12

One of the resistors in this voltage divider circuit is failed open. Based on the voltage readings shown at each load, determine which one it is:

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Question 13

One of the resistors in this voltage divider circuit has failed (either open or shorted). Based on the voltage readings shown at each load, comparing what each load voltage is versus what it should be, determine which resistor has failed and what type of failure it is:

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Question 14

Determine whether or not a shock hazard exists for a person standing on the ground, by touching any one of the points labeled in this circuit:

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Question 15

One of the resistors in this voltage divider circuit has failed (either open or shorted). Based on the voltage readings shown at each load, comparing what each load voltage is versus what it should be, determine which resistor has failed and what type of failure it is:

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Question 16

Question 17

Calculate the amount of voltage between points A and B in this circuit. Be sure to identify polarity as well as magnitude:

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Question 18

Complete the table of values for this circuit:

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Question 19

Complete the table of values for this circuit:

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Question 20

Rank these three light bulb assemblies according to their total electrical resistance (in order of least to greatest), assuming that each of the bulbs is the same type and rating:

Explain how you determined the relative resistances of these light bulb networks.

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Question 21

Identify which of these components are connected directly in series with each other, and which are connected directly in parallel with each other:

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Question 22

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.

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Question 23

Which components are guaranteed to share the exact same voltage by virtue of their connections with each other? Which components are guaranteed to share the exact same current by virtue of their connections with each other?

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Question 24

Rank these five light bulb assemblies according to their total electrical resistance (in order of least to greatest), assuming that each of the bulbs is the same type and rating:

Explain how you determined the relative resistances of these light bulb networks.

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Question 25

Calculate the voltage drops \(V_{AB}\), \(V_{BC}\), and \(V_{CD}\) in the following circuit:

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Question 26

Calculate the amount of voltage dropped across resistor \(R_2\):

Also, note the direction of current through it and the polarity of the voltage drop across it.

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Question 27

Complete the table of values for this circuit:

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Question 28

Draw an equivalent schematic diagram for this circuit, then calculate the voltage dropped by each of these resistors, given a battery voltage of 9 volts. The resistor color codes are as follows (assume 0/ error on all resistor values):

\(R_1 =\) Brn, Grn, Red, Gld

\(R_2 =\) Yel, Vio, Org, Gld

\(R_3 =\) Red, Grn, Red, Gld

\(R_4 =\) Wht, Blk, Red, Gld

\(R_5 =\) Brn, Blk, Org, Gld

Compare the voltage dropped across R1, R2, R3, and R4, with and without R5 in the circuit. What general conclusions may be drawn from these voltage figures?

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Question 29

Calculate both the total resistance of this voltage divider circuit (as "seen" from the perspective of the 25 volt source) and its output voltage (as measured from the \(V_{out}\) terminal to ground):

Note that all potentiometers in this circuit are set exactly to mid-position (50/, or \(m = 0.5\)).

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Question 30

Complete the table of values for this circuit:

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Question 31

Calculate both the total resistance of this voltage divider circuit (as "seen" from the perspective of the 25 volt source) and its output voltage (as measured from the \(V_{out}\) terminal to ground):

Note that the two 5 k\(\Omega\) potentiometers are set to their 80/ positions (\(m = 0.8\)), while the 100 k\(\Omega\) potentiometer is set exactly to mid-position (50/, or \(m = 0.5\)).

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Question 32

Size the resistor in this voltage divider circuit to provide 5 volts to the load, assuming that the load will draw 75 mA of current at this voltage:

As part of your design, include the power dissipation ratings of both resistors.

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Question 33

Size the resistor in this voltage divider circuit to provide 3.2 volts to the load, assuming that the load will draw 10 mA of current at this voltage:

As part of your design, include the power dissipation ratings of both resistors.

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Question 34

Size both resistors in this voltage divider circuit to provide 6 volts to the load, assuming that the load will draw 7 mA of current at this voltage, and to have a "bleeder" current of 1 mA going through \(R_2\):

As part of your design, include the power dissipation ratings of both resistors.

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Question 35

What will happen to the voltages across resistors R1 and R2 when the load is connected to the divider circuit?

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Question 36

Which voltage divider circuit will be least affected by the connection of identical loads? Explain your answer.

What advantage does the other voltage divider have over the circuit that is least affected by the connection of a load?

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Question 37

Suppose you tried to measure the voltage at test point 2 (TP2) with a digital voltmeter having an input resistance of 10 M\(\Omega\). How much voltage would it indicate? How much voltage should it ideally indicate?

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Question 38

What would happen to the voltage drops across each resistor in this circuit if resistor R1 were to fail open?

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Question 39

What will happen to each resistor’s voltage and current in this circuit if resistor R2 fails shorted? Provide individual answers for each resistor, please.

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Question 40

Determine whether or not a shock hazard exists for a person standing on the ground, by touching any one of the points labeled in this faulted circuit:

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Question 41

Explain what will happen to the first load’s voltage and current in this voltage divider circuit if the second load develops a short-circuit fault:

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Question 42

One of the resistors in this voltage divider circuit is failed open. Based on the voltage readings shown at each load, determine which one it is:

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Question 43

One of the resistors in this voltage divider circuit is failed (either open or shorted). Based on the voltage readings shown at each load, determine which one and what type of failure it is:

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Question 44

One of the resistors in this voltage divider circuit has failed (either open or shorted). Based on the voltage readings shown at each load, comparing what each load voltage is versus what it should be, determine which resistor has failed and what type of failure it is:

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Question 45

One of the resistors in this voltage divider circuit has failed (either open or shorted). Based on the voltage readings shown at each load, comparing what each load voltage is versus what it should be, determine which resistor has failed and what type of failure it is:

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Answer 1

Connected directly in series: Battery, R1, and SW1. Connected directly in parallel: Neon lamp and L1.

Answer 2

Bulbs "A" and "C" will glow brightly, while bulbs "B" and "D" will glow dimly.

Answer 3

Answer 4

Rather than tell you each voltage drop, I’ll give you this one hint: there is only one resistor in this breadboard circuit that has voltage across it! All the other resistors in this circuit are de-energized, thanks to the misplacement of resistor R3.

Answer 5

Answer 6

\(V_{AD} = 7.31 { volts}\), 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 k\(\Omega\) resistor would go to zero if the 1.5 k\(\Omega\) resistor were to fail open.

Answer 7

\(I_{total} = 4.69 { mA}\)

Follow-up question: explain why the voltage across the 1500 \(\Omega\) resistor would remain unchanged if the 4700 \(\Omega\) resistor were to fail open.

Challenge question: what crucial assumptions underlie the calculated figure for current shown here? In other words, what unknown quantities can affect the accuracy of our predicted current value?

Answer 8

Answer 9

\(R_{total}\) = 9.978 k\(\Omega\)

\(V_{out}\) = 12.756 V

Answer 10

Answer 11

If resistor R4 fails shorted . . .

Follow-up question: resistors are actually far less likely to fail shorted as they are to fail open. However, this does not mean something else on a circuit board cannot go wrong to make it appear as though a resistor failed shorted! One example of such a fault is called a solder bridge. Explain what this is, any why it could produce the same effect as a resistor failing shorted.

Answer 12

Resistor R2 has failed open.

Answer 13

Resistor \(R_3\) has failed shorted.

Answer 14

Answer 15

Resistor \(R_4\) has failed open.

Answer 16

Additional Practice Problems

Answer 17

\(V_{\bf AB}\) = 9.198 volts, A positive and B negative.

Answer 18

Answer 19

Answer 20

Answer 21

Connected directly in series: Battery and R1.

Connected directly in parallel: Lamp, C1, and D1

Answer 22

Figure 1:

R2 in parallel with R3.

Figure 2:

R1 in series with R2.

Figure 3:

R2 in series with R3.

Figure 4:

R1 in series with R2; R3 in series with R4.

Figure 5:

R1 in parallel with R3; R2 in parallel with R4.

Figure 6:

R1 in series with R2.

Answer 23

The lamp, C1, and D1 are all guaranteed to share the exact same voltage. The battery and R1 are both guaranteed to share the exact same current.

Answer 24

Answer 25

\(V_{AB} = 461 { mV}\)

\(V_{BC} = 0 { V}\)

\(V_{CD} = 1.039 { V}\)

Follow-up question: explain why the voltage between points A and B (\(V_{AB}\)) would increase if the 1200 \(\Omega\) 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.

Answer 26

\(V_{R2} = 12.11 { volts}\), positive on top and negative on bottom. If you follow conventional flow notation, this means current goes down through resistor \(R_2\). The actual flow of electrons through \(R_2\), however, is up.

Answer 27

Answer 28

With R5 in the circuit: & Without R5 in the circuit: \(E_{R1} = 0.226\) volts & \(E_{R1} = 0.225\) volts \(E_{R2} = 7.109\) volts & \(E_{R2} = 7.05\) volts \(E_{R3} = 0.303\) volts & \(E_{R3} = 0.375\) volts \(E_{R4} = 1.36\) volts & \(E_{R4} = 1.35\) volts

Answer 29

\(R_{total}\) = 9.762 k\(\Omega\)

\(V_{out}\) = -12.5 V

Answer 30

Follow-up question: how much voltage is present at the node (junction point) where \(R_1\), \(R_2\), and \(R_3\) all connect together, measured with reference to ground?

Answer 31

\(R_{total}\) = 9.762 k\(\Omega\)

\(V_{out}\) = -16.341 V

Answer 32

R = 264 \(\Omega\). The 330 \(\Omega\) resistor must have a power dissipation rating of at least 3 watts, while the 264 \(\Omega\) resistor will fare well even with a (low) power dissipation rating of \({1 \over 8}\) watt.

Answer 33

R = 1 k\(\Omega\). The 470 \(\Omega\) resistor will fare well even with a (low) power dissipation rating of \({1 \over 8}\) watt, though the 1 k\(\Omega\) resistor will need to be rated in excess of 1/4 watt.

Answer 34

\(R_1 = 750 \> \Omega\) and \(R_2 = 6 { k}\Omega\). \(1 \over 8\) watt resistors are perfectly adequate to handle the dissipations in this circuit.

Answer 35

When the load is connected across R2, R2’s voltage will "sag" (decrease) while R1’s voltage will rise (increase).

Answer 36

The divider circuit with proportionately lower-value resistors will be affected least by the application of a load. The other divider circuit has the advantage of wasting less energy.

Answer 37

Ideally, of course, this voltage divider circuit should exhibit 7.5 volts at test point 2. The voltmeter, however, will register only 6.76 volts.

Follow-up question: is the voltmeter registering inaccurately, or is its connection to the circuit actually changing \(V_{TP2}\)? In other words, what is the actual voltage at TP2 with the voltmeter connected as shown?

Answer 38

If resistor R1 were to fail open (internally), it would drop the full battery voltage across its terminals, leaving no voltage for R2 or R3.

Answer 39

If resistor R2 fails shorted . . .

Follow-up question: note the order in which I list the qualitative effects of R2’s shorted failure. Reading from the top of the list to the bottom reveals the sequence of my reasoning. Explain why I would come to the conclusions I did, in the order I did.

Answer 40

Answer 41

Ideally, the first load’s voltage and current will remain unaffected by any fault within load #2. However, in the event of a short-circuit in load #2, the source voltage will almost surely decrease due to its own internal resistance. In fact, it would not be surprising if the circuit voltage decreased almost to zero volts, if it is a "hard" short in load #2!

Answer 42

Resistor R1 has failed open.

Answer 43

Resistor R1 has failed shorted.

Follow-up question: note that the voltage at load #2 is not fully 25 volts. What does this indicate about the nature of R1’s failure? Be as specific as you can in your answer.

Answer 44

Resistor \(R_2\) has failed open.

Answer 45

Resistor \(R_3\) has failed open.

Kuphaldt, Tony. "Socratic Electronics." Socratic Electronics. Ibiblio.org, n.d. Web. 28 Dec. 2014.

Kuphaldt, Tony. "Socratic Instrumentation." Socratic Instrumentation. Ibiblio.org, n.d. Web. 29 Jan. 2016.

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