recall and use the principle of the potentiometer as a means of comparing potential differences

Potential Dividers – The Potentiometer

What is a Potential Divider?

Think of a potentiometer as a “voltage ruler” that lets you measure unknown voltages without touching the circuit. It works by dividing a known voltage across a resistive wire so that the voltage at any point on the wire is proportional to the distance from the ends. ⚡️

Principle of the Potentiometer

The key idea is that the potential difference between two points on a uniform resistive wire is proportional to the length of the wire between them:

\$ V{AB} = V{AB}^{\text{total}} \times \frac{l_{AB}}{L} \$

Where \$V{AB}^{\text{total}}\$ is the total voltage across the whole wire, \$l{AB}\$ is the distance between points A and B, and \$L\$ is the total length of the wire. This is exactly the same as a simple voltage divider but with a continuous range of points. 🎯

Construction of a Potentiometer

  • Uniform resistive wire (often a carbon track) of length \$L\$.

  • Two contacts: one at the end of the wire (fixed), one movable (slider).

  • Reference voltage source (usually a high‑voltage DC supply) applied across the wire.

  • Unknown voltage source (the one we want to measure) connected to the slider.

  • Null detector (a sensitive ammeter or galvanometer) to detect zero current.

How It Works

  1. Apply a known voltage \$V_{\text{ref}}\$ across the wire.

  2. Move the slider until no current flows through the null detector.

  3. At this point, the voltage at the slider equals the unknown voltage \$V_{\text{unknown}}\$.

  4. Measure the position of the slider to find the ratio \$l/L\$.

  5. Use the proportionality equation to calculate \$V_{\text{unknown}}\$:

\$ V{\text{unknown}} = V{\text{ref}} \times \frac{l}{L} \$

Example Problem

A 10 V reference voltage is applied across a 2 m long potentiometer. The slider is positioned 0.75 m from the zero end when the null detector reads zero. What is the unknown voltage?

Solution:

\$ V_{\text{unknown}} = 10\,\text{V} \times \frac{0.75\,\text{m}}{2\,\text{m}} = 3.75\,\text{V} \$

Exam Tips

  • Always state the proportionality relationship clearly: \$V = V_{\text{ref}}\frac{l}{L}\$.

  • Show the steps of finding the ratio \$l/L\$ before plugging into the formula.

  • Remember that the null detector must read zero current – this is the key condition.

  • Check units: lengths in meters, voltages in volts.

  • Use a diagram if possible – a simple sketch of the potentiometer helps the examiner see you understand the setup.

Summary

The potentiometer is a powerful tool for measuring unknown voltages by exploiting the linear relationship between voltage and distance on a uniform resistive wire. By setting the null detector to zero current, you can determine the exact position of the slider and thus the unknown voltage with high precision. Keep the proportionality equation handy and practice sketching the circuit – you’ll ace the exam! 🚀