Resistors/Spring Constant

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In summary, the formulas for calculating the overall spring constant of springs in series and parallel are similar to the formulas for calculating the total resistance of resistors in parallel and series. This is because the mathematical behavior is the same, even though there are no physical similarities between forces and currents. However, the formulas are not interchangeable as the physical properties of springs and resistors are different. The same mathematical behavior can also be observed with capacitors, if the configurations are reversed. Therefore, the similarity in formulas does not imply physical similitude.
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Hey, i am about to undertake an EPI at school in which i will be testing the spring constants of singular springs, and then of a few springs, both in parrallel and in series.

Before i start the prac i noticed that the equations for the overall spring constant of springs in series/parrallel are opposite to the equations for resistors in series/parrallel... i.e the equation for spring constant in series is the same as that for the resistors in parrallel.

What significance does this hold, if any?

Thanks for any input

-Spoon
 
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  • #2
The formulas are similar because the mathematical behavior is the same. There are no physical similarities.

For two springs in parallel, the total force is the sum of each two forces. For resistors, the total current is the sum of the two currents. Formulas are similar, but you cannot assimilate forces to currents.
 
  • #3
sorry I am not sure that i understand your explanation... if the sum of the forces in parrallel for a spring is just sprinbg one plus spring 2 etc... if the resistor equation works of the same principal would the equation for resistors in parrallel also be the resistance 1 plus resistance 2...it isn't however.. 1/R total = 1/R1 + 1/R2

Could you please try and explain again I am sorry i think i have just mis understood

Thanks

Spoon
 
  • #4
In the case of two springs in parallel, when you stretch the two springs of the same amount (L) the total force will be:
Ft=F1+F2= Lk1+Lk2=Lkt
Then:
kt=k1+k2
For resistors, if a current I traverse the two resistors in series the voltage at the ends of two resistors will be:
Vt=V1+V2=IR1+IR2=IRt
Then:
Rt=R1+R2
You can do the same derivation imposing a force to two springs in series and imposing a voltage to two resistors in parallel.

The formulas are similar for (springs in parallel and resistors in series) and for (springs in series and resistors in parallel)

Same mathematical behavior does not mean physical similitude.
 
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  • #5
It works for capacitors too, if you reverse 'series' and 'parallel'.
 

What is the purpose of a resistor?

A resistor is an electronic component that is used to control the flow of electric current in a circuit. It is designed to resist the flow of electricity and reduce the voltage or current to a desired level.

How do resistors work?

Resistors work by converting electrical energy into heat. They are made of materials that have a high resistance to electric current, such as carbon or metal. When an electric current passes through a resistor, the electrons collide with the atoms in the material, causing them to vibrate and produce heat.

What is the unit of measurement for resistance?

The unit of measurement for resistance is ohms (Ω). One ohm is equal to the resistance that allows one ampere of current to flow through a conductor when one volt of potential difference is applied.

How is the spring constant of a resistor determined?

The spring constant of a resistor is determined by the material it is made of and its physical dimensions. It is calculated by dividing the change in force by the change in length of the resistor. The resulting unit is Newtons per meter (N/m).

What factors affect the spring constant of a resistor?

The spring constant of a resistor is affected by the material it is made of, its physical dimensions, and its temperature. Different materials have different resistivities, which can affect the resistance and therefore the spring constant. The length, cross-sectional area, and temperature of the resistor also play a role in determining the spring constant.

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