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Lesson 8.5 • Competency 8.5Complete Lesson
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Potentiometer & Bridge Circuits

Potential divider principle, uniform potentiometer wire and potential gradient k = V/l, comparison of cell EMFs (E₁/E₂ = l₁/l₂), cell internal resistance determination r = R(l₀ - l)/l, Wheatstone Bridge balance condition P/Q = R/S, and the Meter Bridge.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Explain why a potentiometer achieves ideal null-balance voltage measurements without drawing current from the test source.
  • Calculate cell EMFs and determine cell internal resistance using potentiometer balance lengths: r = R(l₀ - l)/l.
  • Derive the Wheatstone Bridge balance condition (P/Q = R/S) and apply the Meter Bridge to measure unknown resistances and temperature coefficients.

Core Theory & Concepts

High-precision electrical metrology relies on null-deflection balance techniques. Because ordinary meters draw current and perturb the circuit under test, null-detecting instruments like the Potentiometer and Wheatstone Bridge balance opposing voltages or bridge ratios until zero current flows through a sensitive detector, eliminating loading errors entirely.

Potentiometer Internal Resistance Method

Open-circuit balance length l₀ measures EMF E. Shunted balance length l with resistor R measures terminal voltage V: r = R ((l₀ - l) / l).

r = R \left( \frac{l_0 - l}{l} \right)

Wheatstone Bridge Balance Condition

When the potential difference across the galvanometer is zero (null deflection): P / Q = R / S => S = (Q R) / P.

\frac{P}{Q} = \frac{R}{S} \quad \Longleftrightarrow \quad S = \frac{Q \cdot R}{P}

Common Misconceptions

Misconception

The potentiometer wire must be made of low-resistance copper to minimize heat.

Physical Clarification:The potentiometer wire requires high resistivity and a nearly zero temperature coefficient of resistance (like manganin or constantan) so that resistance per unit length remains strictly uniform and unaffected by current-induced temperature shifts.

Syllabus Topic Outline

Competency 8.5
  • 1Potential divider circuit formula: V_out = V_in * (R₂ / (R₁ + R₂))
  • 2Potentiometer wire uniformity and potential gradient k = V_wire / L
  • 3Comparison of EMFs of two cells using potentiometer balance lengths
  • 4Determination of internal resistance of a cell (open vs shunted balance)
  • 5Wheatstone Bridge principle: derivation of null condition P / Q = R / S
  • 6Meter Bridge practical: end-error correction and sensitivity optimization at 50 cm