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Potentiometer: Principle and Applications Easy Explanation

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A potentiometer is a long uniform wire (often 10 m) along which a steady potential drops gradually. It compares voltages by a null method: a known potential fall along the wire is balanced against an unknown electromotive force (EMF), so no current is drawn from the cell being measured.

It matters because an ordinary voltmeter draws current and measures terminal potential difference, not the true EMF. The potentiometer measures EMF fairly, compares two cells, and finds internal resistance very accurately — essential for cells, sensors and calibration work.

Key Concepts

Potential gradient k: fall of potential per unit length, k = V/L, unit volt per metre (V/m). Driver cell: stronger cell that maintains constant current through the wire. Balance length l: length from the positive end to the null or jockey point. EMF ε: total work done per unit charge by the source, unit volt (V). Internal resistance r: resistance inside the cell, unit ohm (Ω).

Formulas

ε = k l where ε in V, k in V/m and l in metre (m). Comparison of EMFs: ε1/ε2 = l1/l2 because k cancels for the same wire current. Internal resistance: r = R × (l1 − l2)/l2 where R is external resistance in Ω, l1 is balance length for EMF (open circuit) and l2 is balance length for terminal voltage with R connected. Assumption: driver current and wire uniformity stay constant during measurement. Limit: if the EMF exceeds the total potential across the wire, no balance point exists.

Worked Example

A potentiometer wire has k = 0.01 V/cm. With a cell, balance is at l1 = 150 cm open-circuit, and with R = 10 Ω across it, balance is at l2 = 120 cm.

  1. EMF ε = k l1 = 0.01 × 150 = 1.5 V.
  2. Apply r = R × (l1 − l2)/l2 = 10 × (150 − 120)/120.
  3. r = 10 × 30/120 = 2.5 Ω.

The cell has EMF 1.5 V and internal resistance 2.5 Ω, which explains why its terminal voltage falls under load.

Common Misconceptions

  • A voltmeter and potentiometer measure the same thing: A voltmeter always draws current and shows terminal voltage; the potentiometer at null draws none and shows true EMF.
  • Balance length depends on the standard cell only: It also depends on potential gradient, so changing driver voltage or wire resistance shifts every balance length.
  • Longer wire is always better: A longer wire lowers k and raises sensitivity, but only if the driver can maintain a steady current without heating.

Real-World Applications

  • Comparing EMFs of primary cells and calibrating voltmeters and ammeters.
  • Measuring internal resistance of batteries in laboratories.
  • Precise low-voltage measurements in thermocouple and sensor circuits.

The potentiometer turns voltage measurement into a length measurement at zero current, giving true EMF, fair comparison of cells, and a clean way to find internal resistance.

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