How do I calculate Vo/Vs for a potentiometer circuit with varying resistance?

In summary, the wiper in the given circuit divides the potentiometer resistance between \alpha R and (1-\alpha R) where 0 \leq\alpha \geq 1. Using KVL and KCL, the voltage ratio can be calculated as ((\SigmaR)/I)Vs, where R is the total resistance of the potentiometer. The resistance of the main part of the pot to ground below the wiper can be ignored as it is in parallel with a short circuit. The resistance of the pot can be simplified to R(1-\alpha).
  • #1
tanky322
43
0

Homework Statement


In the circuit below, the wiper divides the potentiometer resistance between [tex]\alpha R[/tex] and[tex]\ (1- alpha R)[/tex], 0 [tex]\leq[/tex][tex]\alpha[/tex] [tex]\geq 1[/tex]. Find Vo / Vs

Schematic1.jpg

Homework Equations



KVL
KCL

The Attempt at a Solution



Im thinking that the Pot. Resistance will be R +(1-[tex]\alpha[/tex])R. Then to find the voltage (R +(1-[tex]\alpha[/tex])R)I
 

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  • #2
You can ignore the resistance of the main part of the pot to ground that is below the wiper because it is in parallel with a short circuit.
The resitance of the pot is simply, R - alphaR = R(1-alpha)
 
  • #3
So would the answer be:

(([tex]\Sigma[/tex]R)/I)Vs


Sorry about the formatting, I need to learn how to use the system.


Thanks


Andrew
 

FAQ: How do I calculate Vo/Vs for a potentiometer circuit with varying resistance?

What is a potentiometer resistance?

A potentiometer resistance is the measure of opposition to the flow of electric current through a potentiometer. It is dependent on the material and dimensions of the potentiometer and is typically measured in ohms (Ω).

How does potentiometer resistance affect circuit performance?

Potentiometer resistance can impact the performance of a circuit in several ways. It can affect the amount of current flowing through the circuit, the accuracy of voltage measurements, and the stability of the circuit. Too high or too low resistance can result in faulty readings or even damage to the circuit.

What factors can affect potentiometer resistance?

Potentiometer resistance can be affected by several factors, including the material and dimensions of the potentiometer, the temperature, and the amount of current flowing through the circuit. The type of potentiometer used and the way it is connected in the circuit can also impact the resistance.

How can potentiometer resistance be measured?

Potentiometer resistance can be measured using a multimeter or an ohmmeter. To measure the resistance, the potentiometer must be disconnected from the circuit and the two test leads of the multimeter should be connected to the two ends of the potentiometer. The measured value will be the potentiometer resistance in ohms (Ω).

What is the difference between fixed and variable potentiometer resistance?

Fixed potentiometer resistance is a predetermined value that cannot be changed, while variable potentiometer resistance can be adjusted to a desired value. Variable potentiometers have a movable contact that allows the user to change the resistance, while fixed potentiometers have a fixed contact and are typically used for specific purposes in a circuit.

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