The potentiometer

Section: D.C. Circuits  |  Syllabus: Cambridge AS Level Physics (9702)

The Potentiometer

A potentiometer is a device used to measure or compare potential differences with high accuracy. It works on the principle of a potential divider but uses a continuous wire instead of discrete resistors.

Potentiometer An instrument that compares an unknown p.d. or e.m.f. with a known p.d. by finding the position along a uniform wire where no current flows through a galvanometer (null point).

Construction

A slide-wire potentiometer consists of:

FIG 10.19: Slide-Wire Potentiometer Circuit

Show a circuit with: A driver cell connected across a uniform wire XZ (marked with a metre scale). Point X at one end, Z at the other. A sliding contact (jockey) at point Y along the wire. The unknown e.m.f. (cell being tested) connected with its positive terminal to X. A galvanometer (G) connected between the negative terminal of the test cell and the jockey. Label the length l = XY and show that both positive terminals connect to the same point X.

Principle of Operation

The wire acts as a continuous potential divider. If the wire has uniform cross-sectional area and resistivity, its resistance is proportional to its length:

R ∝ l (for uniform wire)

Therefore, for a constant current through the wire, the p.d. across any section is proportional to its length:

V ∝ l

Balancing the Potentiometer

The jockey is moved along the wire until the galvanometer shows zero deflection (the null point). At this point:

Balance Condition At the null point: _unknown = (l/L) × V_driver

where l = balance length (XY), L = total wire length (XZ), V_driver = p.d. across the whole wire

Since V ∝ l along a uniform wire with constant current:

_unknownV_driver = (l/L)

The Galvanometer

Galvanometer A sensitive current-detecting instrument that can measure very small currents and indicate their direction. It has a centre-zero scale, with the pointer deflecting left or right depending on current direction.

Use in Null Methods

In a potentiometer, the galvanometer is used as a null detector - we only need to know when the current through it is zero, not the actual value of any current.

Advantages of using a galvanometer in null methods:

Null Methods and Their Advantages

Null Method A measurement technique in which the quantity being measured is compared against a standard, and the measurement is made when a detector shows zero (null) reading.

Why Null Methods Give More Accurate Measurements

When the potentiometer is balanced (galvanometer reads zero):

  1. No current flows through the cell being tested
    • Therefore there is no p.d. drop across its internal resistance
    • The measured value equals the true e.m.f., not the terminal p.d.
  2. No current flows through the galvanometer
    • The galvanometer's resistance does not affect the measurement
    • Eliminates systematic errors from the measuring instrument
Key Advantage

A voltmeter always draws some current from the circuit it measures, so it measures terminal p.d. rather than true e.m.f. A potentiometer at balance draws zero current, so it measures the true e.m.f. This makes it more accurate than a voltmeter for measuring e.m.f.

Comparing Two E.m.f.s

A potentiometer can compare two unknown e.m.f.s by finding the balance length for each:

Comparing E.m.f.s (_1/_2) = (l_1/l_2)

where l_1 and l_2 are the balance lengths for e.m.f.s _1 and _2 respectively

This ratio method eliminates the need to know the p.d. across the driver cell or the resistance per unit length of the wire.

Worked Example: Comparing E.m.f.s

Problem: A standard cell of e.m.f. 1.018 V balances at 50.9 cm on a potentiometer wire. An unknown cell balances at 75.2 cm. What is the e.m.f. of the unknown cell?

Solution:

_unknown_standard = l_unknownl_standard _unknown1.018 = (75.2/50.9) _unknown = 1.018 × (75.2/50.9) = 1.018 × 1.477 _unknown = 1.50 V Worked Example: Direct E.m.f. Measurement

Problem: A potentiometer wire XZ is 1.00 m long. The variable resistor is adjusted so that there is a p.d. of 1.50 V across the full length of the wire. The galvanometer reads zero when the movable contact is positioned 47.6 cm from point X. What is the e.m.f. of the cell being tested?

Solution:

Since p.d. is proportional to length along a uniform wire: V_wire = (l/L) = (l/L) × V_wire = (47.6/100) × 1.50 = 0.476 × 1.50 = 0.714 V

Ideal Properties of Measuring Instruments

The limitations of real measuring instruments can introduce errors. Ideal instruments would have the following properties:

Instrument Ideal Property Reason
Ammeter Zero resistance So it does not reduce the current it is measuring or add to the total circuit resistance
Voltmeter Infinite resistance So it draws no current from the circuit and does not affect the p.d. it is measuring
Galvanometer (in null methods) High sensitivity So it can detect very small currents and locate the null point precisely
Why This Matters

A real ammeter has some resistance, which reduces the current being measured. A real voltmeter has finite resistance, so it draws current and measures a lower value than the true p.d. These effects are called loading errors. Null methods avoid loading errors because at balance, no current flows through the detector.

The Wheatstone Bridge

The null method principle extends beyond the potentiometer. In a Wheatstone bridge, four resistors are arranged in a diamond pattern with a galvanometer across the middle.

FIG 10.20: Wheatstone Bridge Circuit

Show a diamond-shaped circuit with four resistors: R₁ (top-left), R₂ (top-right), R₃ (bottom-left), R₄ (bottom-right). A galvanometer connects the middle junctions (between R₁-R₂ and R₃-R₄). A power supply connects top to bottom. Label that when the galvanometer shows no deflection, the bridge is balanced.

When the galvanometer shows no deflection (null point), the p.d.s across the two branches are balanced, and:

(R_1/R_2) = (R_3/R_4)

This allows an unknown resistor to be determined from three known resistances.

Experimental Techniques

When using a potentiometer, careful experimental technique improves accuracy:

Practical Tips

Interactive revision notes, videos and practice questions load below.

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