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The answers to this question may seem paradoxical to students: the lowest value of resistor dissipates the greatest power. Math does not lie, though.
Another purpose of this question is to instill in students' minds the concept of components in a simple parallel circuit all sharing the same amount of voltage.
Challenge your students to recognize any mathematical patterns in the respective currents and power dissipations. What can be said, mathematically, about the current drawn by the 2 W resistor versus the 1 W resistor, for example?
You might want to mention that in electrical parlance, a "heavy" load is one that draws a large amount of current, and thus has a large resistance. This circuit, which shows how the lowest resistance in a parallel circuit consumes the most power, gives practical support to the term "heavy" used to describe loads.

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Notes:
This question illustrates a disparity between the ideal conditions generally assumed for theoretical calculations, and those conditions encountered in real life. Truly, it is the purpose of a voltage source to maintain a constant output voltage regardless of load (current drawn from it), but in real life this is nearly impossible. Most voltage sources exhibit some degree of ßag" in their output over a range of load currents, some worse than others.
In this example, it is impossible to tell how much the voltage source's output will ßag" when the switch is closed, because we have no idea of what the resistor's current draw will be compared to that of the light bulb, or what the voltage source's rated output current is. All we can say is that theoretically there will be no effect from closing the switch, but that in real life there will be some degree of dimming when the switch is closed.

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It has been my experience that students require much practice with circuit analysis to become proficient. To this end, instructors usually provide their students with lots of practice problems to work through, and provide answers for students to check their work against. While this approach makes students proficient in circuit theory, it fails to fully educate them.
Students don't just need mathematical practice. They also need real, hands-on practice building circuits and using test equipment. So, I suggest the following alternative approach: students should build their own "practice problems" with real components, and try to mathematically predict the various voltage and current values. This way, the mathematical theory "comes alive," and students gain practical proficiency they wouldn't gain merely by solving equations.
Another reason for following this method of practice is to teach students scientific method: the process of testing a hypothesis (in this case, mathematical predictions) by performing a real experiment. Students will also develop real troubleshooting skills as they occasionally make circuit construction errors.
Spend a few moments of time with your class to review some of the "rules" for building circuits before they begin. Discuss these issues with your students in the same Socratic manner you would normally discuss the worksheet questions, rather than simply telling them what they should and should not do. I never cease to be amazed at how poorly students grasp instructions when presented in a typical lecture (instructor monologue) format!
A note to those instructors who may complain about the "wasted" time required to have students build real circuits instead of just mathematically analyzing theoretical circuits:
                    What is the purpose of students taking your course?
If your students will be working with real circuits, then they should learn on real circuits whenever possible. If your goal is to educate theoretical physicists, then stick with abstract analysis, by all means! But most of us plan for our students to do something in the real world with the education we give them. The "wasted" time spent building real circuits will pay huge dividends when it comes time for them to apply their knowledge to practical problems.
Furthermore, having students build their own practice problems teaches them how to perform primary research, thus empowering them to continue their electrical/electronics education autonomously.
In most sciences, realistic experiments are much more difficult and expensive to set up than electrical circuits. Nuclear physics, biology, geology, and chemistry professors would just love to be able to have their students apply advanced mathematics to real experiments posing no safety hazard and costing less than a textbook. They can't, but you can. Exploit the convenience inherent to your science, and get those students of yours practicing their math on lots of real circuits!

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This question is an exercise in basic algebra, specifically the meaning of negative exponents.

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This question is really nothing more than an exercise in algebraic manipulation.

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This question is nothing more than practice algebraically manipulating equations. Ask your students to show you how they solved it, and how the two given answers are equivalent.

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The purpose of this question is to get students to identify what distinguishing characteristic uniquely identifies a circuit as being "parallel." Once this has been identified, there are several conclusions which may be deduced (regarding voltage drops, currents, resistances, etc.).
Some students may have difficulty distinguishing that circuit E is a parallel circuit, but it is!

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The hint suggesting identification of electrically common points is critical to students' understanding of parallel circuits. Once they see that there is no difference (as far as voltage is concerned) between the top of one resistor, the top of the other, or the top of the battery (and likewise for all the bottom connections), it should become clearly evident why voltage must be equal across these three components.

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A key element to this question is the plotting of currents. Students need to see how individual resistor currents graphically relate to the total source current in a parallel circuit, because this has direct bearing on the calculation of total current, and also to an understanding of total resistance in parallel circuits.

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Here, the important principles of voltage and current in a parallel circuit are highlighted. This question serves to further define, in practical ways, what the term "parallel" really means.
An important lesson of this question is the distinction between measurements which are guaranteed to be equal versus measurements which just happen to be equal for a given selection of components.

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While some students seem able to immediately grasp the concept of parallel resistances diminishing in (total) value, it is worthwhile to approach it from an Ohm's Law perspective as well to give other students a more formal rationale for this effect.

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The concept of parallel (total) resistance, in relation to individual resistances, often confuses new students. Be sure to allow plenty of discussion time to work through the conceptual difficulties with them.

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Although I typically use the lower formula exclusively in my teaching, the upper formula is often useful for situations where a calculator is not handy, and you must estimate parallel resistance.

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Once students recognize the mathematical relationship between resistance and conductance (G = ¹/_R), and they realize that parallel conductances add just like series resistances add, it is but a short exercise in algebra to develop the parallel resistance formula (R_parallel = [1/( [1/(R₁)] + [1/(R₂)] + �[1/(R_n)] )]).

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I_R1 = 12 mA ; V_R1 = 12 V

I_R2 = 5.45 mA ; V_R2 = 12 V

I_R3 = 25.5 mA ; V_R3 = 12 V

Notes:
Students often just want to memorize a procedure for determining answers to questions like these. Challenge your students to not only understand the procedure, but to also explain why it must be followed.
Something your students will come to realize in discussion is that there is more than one way to arrive at all the answers! While some of the steps will be common to all calculation strategies, other steps (near the end) leave room for creativity.

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Discuss with your students what a good procedure might be for calculating the unknown values in this problem, and also how they might check their work.

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Discuss with your students what a good procedure might be for calculating the unknown values in this problem, and also how they might check their work.

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Rules of series and parallel circuits are very important for students to comprehend. However, a trend I have noticed in many students is the habit of memorizing rather than understanding these rules. Students will work hard to memorize the rules without really comprehending why the rules are true, and therefore often fail to recall or apply the rules properly.
An illustrative technique I have found very useful is to have students create their own example circuits in which to test these rules. Simple series and parallel circuits pose little challenge to construct, and therefore serve as excellent learning tools. What could be better, or more authoritative, than learning principles of circuits from real experiments? This is known as primary research, and it constitutes the foundation of scientific inquiry. The greatest problem you will have as an instructor is encouraging your students to take the initiative to build these demonstration circuits on their own, because they are so used to having teachers simply tell them how things work. This is a shame, and it reflects poorly on the state of modern education.

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Notes:
One problem I've encountered while teaching the "laws" of parallel circuits is that some students mistakenly think the rule of äll voltages in a parallel circuit being the same" means that the amount of voltage in a parallel circuit is fixed over time and cannot change. The root of this misunderstanding is memorization rather than comprehension: students memorize the rule "all voltages are the same" and think this means the voltages must remain the same before and after any change is made to the circuit. I've actually had students complain to me, saying, "But you told us all voltages are the same in a parallel circuit!", as though it were my job to decree perfect and universal Laws which would require no critical thinking on the part of the student. But I digress . . .
This question challenges students' comprehension of parallel circuit behavior by asking what happens after a change is made to the circuit. The purpose of the switches is to ädd" resistors from the circuit, one at a time, without actually having to insert new components.

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�

Current through the 2 kW resistor = 4.5 mA

�

Current through the 3 kW resistor = 3 mA

�

Current through the 5 kW resistor = 1.8 mA

�

Voltage across each resistor = 9 volts

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R_total = 967.74 W

Notes:
Some students may find the diagram hard to follow, and so they will find the task of analysis helped by drawing an equivalent schematic diagram for this circuit, with all terminal points labeled. I recommend you not suggest this solution immediately, but rather challenge your students to think of problem-solving techniques on their own. Surely, someone in the class will have thought of doing this, and the impact of such a suggestion coming from a peer is greater than if it came from you, the instructor.
Be sure to ask your students this question: "Why is this type of circuit commonly called a current divider?"

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Notes:
And who said technological work never involves creativity? This question challenges students to apply an equation to a problem that it is not ideally suited for. The basic principle used in the solution of the problem is very practical. It involves the substitution of an equivalent component value in place of multiple components, which is a problem-solving technique widely applied in electrical network analysis, as well as other forms of mathematical analysis.

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This problem is an exercise in estimation, and algebraic equation manipulation. Estimation will reveal which resistors should be combined together, and algebraic manipulation will give the exact values needed.

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One of the more difficult visualization tasks for new students of electronics is translating schematic diagrams to physical layouts, and visa-versa. This, sadly, is a skill that I don't see emphasized nearly enough in most basic electronics curricula. It seems the majority of class time is spent mathematically analyzing useless resistor networks, and not enough time is invested building students' spatial relations skills.
While series connections are very easy to visualize on terminal strips, parallel connections are more difficult. Work with your students through this question helping those who lack the innate spatial relations ability to see the solution quickly.
A "trick" I often use to help students build this skill is to have them first draw a nice, clean schematic diagram. Then they over-trace each wire in the diagram as they draw it in the pictorial diagram. In this way, they make sure not to overlook connections in the pictorial diagram.

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Notes:
This is a fine example of a question with multiple correct answers. No matter how many unique combinations students invent, they may all be verified by a few simple Ohm's Law calculations.

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