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## Example Questions

### Example Question #1 : Resistors

You are given three resistors with known values:

You are asked to create a circuit with a total resistance of between and . How should you arrange the resistors to accomplish this?

**Possible Answers:**

, , and in parallel

and in parallel; is not necessary

and in parallel, connected to in series

and in parallel, connected to in series

, , and in series

**Correct answer:**

and in parallel, connected to in series

**This question requires no math to correctly answer!** You should not need to 'brute force' it. Although it is designed to appear time consuming, it should be relatively easily once the principle of resistors in parallel is understood. *Whenever two resistors are connected in parallel, the net resistance must be less than the resistance of either of the two alone*.

*When resistors are connected in series, the net resistance*

**must**be more than the resistance of either alone.*Explanation of correct answer:*

** and in parallel, connected to in series** - It is possible to 'eyeball' this to see that this is at least feasible. and in parallel must make a network with an overall resistance less than . When added in series with (), the overall may fall between and . To confirm, one could do the math to calculate the overall resistance, but the point of this question is to use general principles to quickly eliminate the other, incorrect answer choices.

*Explanations of incorrect answers:*

**, , and in parallel - **This combination cannot possibly work since the overall resistance must be less than (the smallest resistor in parallel).

** and in parallel, connected to in series** - Regardless of the overall resistance of and in parallel, the connection with in series makes the total resistance more than .

** and in parallel; is not necessary **- Placing and in parallel must result in a resistance less than .

**, , and in series** - Connecting resistors in series results in an overall resistance greater than that of any one alone. Since and are included in series, the sum of the resistances is obviously much greater than what we are asked to produce and this choice can be immediately eliminated.

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