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

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SUMMARY

The discussion focuses on calculating the output voltage (Vo) to input voltage (Vs) ratio for a potentiometer circuit with varying resistance, specifically using the variable α to represent the wiper position. The key equation derived is Vo/Vs = (ΣR/I)Vs, where R is the total resistance and I is the current. The analysis incorporates Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) to simplify the circuit's resistance calculations. The final expression accounts for the effective resistance of the potentiometer based on the wiper's position.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with Kirchhoff's Current Law (KCL)
  • Basic knowledge of potentiometer circuits
  • Ability to manipulate algebraic expressions involving resistance
NEXT STEPS
  • Study the application of Kirchhoff's Laws in complex circuits
  • Learn about the behavior of potentiometers in series and parallel configurations
  • Explore advanced circuit analysis techniques using Thevenin's and Norton's theorems
  • Investigate the impact of varying resistance on voltage division in circuits
USEFUL FOR

Electrical engineering students, circuit designers, and hobbyists working with potentiometer circuits and voltage calculations will benefit from this discussion.

tanky322
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Homework Statement


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

Schematic1.jpg

Homework Equations



KVL
KCL

The Attempt at a Solution



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

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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)
 
So would the answer be:

((\SigmaR)/I)Vs


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


Thanks


Andrew
 

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