How to arrange given resistors in a given shape to meet target value?

In summary, the student is seeking help in choosing a combination of 5 resistors of different values (10kΩ, 22kΩ, 47kΩ, 100kΩ, and 220kΩ) to create a total resistance of 35kΩ in a U shape. The student is aware of the equations for series and parallel resistors but is unsure how to apply them in this scenario. They suggest using all 10kΩ resistors in series, but this would result in a total resistance of 50kΩ, so they are considering a combination of series and parallel arrangements.
  • #1
Bahamas
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Homework Statement


I have available resistors of 5 different values (10kΩ, 22kΩ, 47kΩ, 100kΩ and 220kΩ).
How can I choose a combination of these resistors that will create a total resistance of 35kΩ in a U shape (using 5 resistors)?
See attached picture of 'U' to get a clear picture of the shape.

Homework Equations


Series Resistors
[R][/eq] = [R][/1]+[R][/2]+[R][/3]+...

Parallel Resistors
1/[R][/eq]=1/[R][/1] + 1/[R][/2] + 1/[R][/3] +...

The Attempt at a Solution


I really don't know here. They would all be in a series for the 'U' shape, so even if I use 5 of the 10kΩ resistors, I will end up with a total resistance of 50kΩ
 

Attachments

  • U.PNG
    U.PNG
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  • #2
It would seem that since a simple series arrangement of the resistors does not give the desired total resistance of 35 k Ohms, you will need to explore an arrangement of resistors in parallel combined with resistors in series to see if a total R = 35 k Ohms can be established.
 

Related to How to arrange given resistors in a given shape to meet target value?

1. How do I determine the correct resistance value for each individual resistor?

The resistance value for each individual resistor can be calculated using Ohm's Law (R = V/I), where R is the resistance value in ohms, V is the target voltage, and I is the desired current. Alternatively, you can use online resistor calculators or refer to a resistor color code chart.

2. Can I use resistors in series or parallel to achieve the target resistance value?

Yes, resistors can be connected in series or parallel to achieve a specific resistance value. In series, the resistance values are added together (R = R1 + R2 + ... + Rn), while in parallel, the inverse of the resistance values are added together and then inverted (1/R = 1/R1 + 1/R2 + ... + 1/Rn).

3. Is there a maximum number of resistors that can be used in a given shape?

There is no specific limit on the number of resistors that can be used in a given shape. However, it is important to consider the physical space and limitations of the shape when determining the number of resistors to use.

4. Can I use different types of resistors (e.g. variable resistors) in the arrangement?

Yes, you can use different types of resistors in the arrangement as long as they have the same target resistance value. However, it is important to consider the tolerance and temperature coefficient of the resistors to ensure accurate results.

5. How do I arrange the resistors in the given shape to meet the target value?

The arrangement of resistors will depend on the specific shape and target resistance value. It is best to start by calculating the resistance value for each individual resistor and then determining the best configuration (series, parallel, or combination) to achieve the target value. You can use circuit simulation software or consult a resistor network calculator for assistance.

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