Measurement of unknown resistance using potentiometer

In summary, the conversation is discussing a potentiometer circuit used to compare two resistances. A standard resistor of 10.0 Ω has a balance point at 58.3 cm, while the unknown resistance X has a balance point at 68.5 cm. The value of X is being determined using a method that involves taking an arbitrary internal resistance into account. However, it is noted that the solution given may be incorrect and further discussion is recommended.
  • #1
Anind
5
0
[Mentor's Note: Thread moved to homework forums from another forum]

Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X.
upload_2015-7-20_14-56-35.png

In the solution of this problem every book using this method:-
upload_2015-7-20_15-3-49.png

my question is how can we take equal i for each resistance?
 

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  • #2
We've seen this arrangement presented before, and for a time it had us purplexed. I believe the conclusion was that the lower-drawn source ε is actually a voltage source having significant resistance. So mark in some fixed internal resistance there, and re-examine the question.

Does your textbook give an explanation of the circuit and its operation, and mentioning that source having internal resistance? Without the recognition of that internal resistance, the circuit makes no sense.
 
  • #3
NascentOxygen said:
We've seen this arrangement presented before, and for a time it had us purplexed. I believe the conclusion was that the lower-drawn source ε is actually a voltage source having significant resistance. So mark in some fixed internal resistance there, and re-examine the question.

Does your textbook give an explanation of the circuit and its operation, and mentioning that source having internal resistance? Without the recognition of that internal resistance, the circuit makes no sense.
i copied the whole question from textbook. nothing was told about internal resistance. in general we have to take an arbitrary internal resistance here.
 
  • #4
Yes, arbitrary, but not zero.
 
  • #5
NascentOxygen said:
Yes, arbitrary, but not zero.
ok if there is a non-zero internal resistance, then what about the current through resistor R and X? are they equal? why? please answer it. I need it very badly.
 
  • #6
Anind said:
ok if there is a non-zero internal resistance, then what about the current through resistor R and X? are they equal? why? please answer it. I need it very badly.
R and X are different valued resistances, so when separately connected to source ε will have different currents.
 
  • #7
In your first post you provided an "explanation" of how the arrangement works. I don't understand that description.
 
  • #8
NascentOxygen said:
R and X are different valued resistances, so when separately connected to source ε will have different currents.
So you agree that the solution given above is wrong right?
 
  • #9
  • #10

What is a potentiometer?

A potentiometer is an electrical instrument used for measuring unknown resistance. It consists of a long resistive element with a sliding contact, or wiper, that can be moved along the resistive element. The resistance between the wiper and one end of the resistive element can be adjusted to match the unknown resistance being measured.

How does a potentiometer measure unknown resistance?

A potentiometer works on the principle of balancing two opposing voltages. One voltage is produced by a known resistance, called the standard resistance, while the other is produced by the unknown resistance being measured. By adjusting the position of the sliding contact, the two voltages can be made equal, allowing the unknown resistance to be calculated.

What are the advantages of using a potentiometer for measuring resistance?

One advantage of using a potentiometer is that it is a highly accurate method of measuring resistance. It also does not require a power source, making it convenient for use in remote locations. Additionally, a potentiometer can measure a wide range of resistances, from a few ohms to several megaohms.

What are some potential sources of error when using a potentiometer?

One potential source of error when using a potentiometer is the introduction of stray resistances in the circuit, which can affect the accuracy of the measurements. Another source of error is the change in resistance due to temperature variations. To minimize these errors, it is important to use high-quality components and keep the potentiometer and standard resistance at a constant temperature.

Can a potentiometer be used to measure resistance in circuits with AC current?

Yes, a potentiometer can be used to measure resistance in both DC and AC circuits. However, in AC circuits, the potentiometer must be calibrated for the frequency of the current being measured, as the impedance of the resistive element can vary with frequency. Additionally, the potentiometer must be connected in series with the circuit, rather than in parallel as in DC circuits.

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