Calculating Resistance of Y with X & Variable Resistor

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    Parallel Resistors
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Discussion Overview

The discussion revolves around calculating the resistance of a resistor (Y) in parallel with another resistor (X) using measurements from a variable resistor, ammeter, and voltmeter. Participants explore the relationships between current, voltage, and resistance in this experimental setup.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes measuring voltage and current to calculate the resistance of resistor X when the switch is open and seeks guidance on calculating Y when the switch is closed.
  • Another participant questions the calculation method that led to a negative number, emphasizing that the total resistance of two parallel resistors should be less than that of the individual resistors.
  • A participant shares their method of varying the variable resistor to obtain multiple current and voltage readings, suggesting a graphical approach to determine resistance.
  • Further clarification is provided that since the total resistance R is less than X, the relationship 1/R should be greater than 1/X, indicating a potential error in calculations.
  • One participant expresses confusion and suggests the possibility of a mistake in plotting or measuring, reinforcing the idea that the total resistance should adhere to established principles of parallel resistors.
  • A later reply acknowledges a mistake in the calculation approach, correcting the order of terms in the equation used to find resistance.

Areas of Agreement / Disagreement

Participants generally agree on the principle that the total resistance of two parallel resistors is less than that of the individual resistors. However, there is disagreement regarding the specific calculations and methods used, with some participants questioning the accuracy of measurements and calculations.

Contextual Notes

There are indications of potential errors in measurement or calculation methods, as well as confusion regarding the plotting of current versus voltage. The discussion does not resolve these issues, leaving some uncertainty in the approach taken by participants.

Who May Find This Useful

This discussion may be useful for individuals interested in experimental physics, particularly those working with electrical circuits and resistance calculations in parallel resistor configurations.

CAH
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I've got two resistors in parallel (X and Y) and a variable resistor, ammeter and voltmeter. SEE PHOTO!

I've calculated the value of X by measuring V and I when the switch is open. I can close the switch and measure V and I but how do I calculate the resistance of Y?

I know 1/x + 1/y = 1/R, this may be a stupid question? When I do 1/R - 1/x (where x is known from previous calculation) I get a negative number.

Thanks
 

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Are you sure 1/R - 1/x gives a negative number? The total resistans of two parallel resistors should always be less than the resistans of the individual ones.

How do you use the variable resistor in your measurments and calculations?
 
I varied the resistor to get values of I from 10mA, 20, 30, 40, 50mA and recorded voltage for each one and then across the parallel I did 10mA, 30, 50, 70, 90mA and recorded V then drew the graphs and used the gradient for resistance of each! :)
 
Since R is less than X, 1/R will be greater than 1/X and you shouldn't be getting a negative number. Set your variable resistor so that you have 10 mA of current with the switch open. Then, without changing the variable resistor close the switch and check your ammeter. What is your current at now?
 
CAH said:
I varied the resistor to get values of I from 10mA, 20, 30, 40, 50mA and recorded voltage for each one and then across the parallel I did 10mA, 30, 50, 70, 90mA and recorded V then drew the graphs and used the gradient for resistance of each! :)

I can't see what's wrong here, but I agree with Drakkith: the total resistance of two resistors in parallel is always less than any resistance of the individual ones, thus 1/R>1/x .
Are you sure you haven't done some little misstake, such as plotting I(U) instead of U(I) or exchanging the two series of measurements? :)
 
Thanks I made a ridiculously stupid mistake: I was doing 1/Rx - 1/Rt insead of 1/Rt - 1/Rx!
 

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