Home › Experiments › Physics Experiments › Measurement of Electrical Resistance of Copper Wire Using Potentiometer - Physics Simplified

Measurement of Electrical Resistance of Copper Wire Using Potentiometer - Physics Simplified

Determine the electrical resistance of a given copper wire using a potentiometer.

Physics Experiments 20 September, 2026 10 min read
Home » Experiments » Resistance of Copper Wire Using Potentiometer

Measurement of Electrical Resistance of Copper Wire Using Potentiometer

Physics Lab Experiment • Class 12 Practical • Potentiometer & Resistance Measurement

Aim

To determine the electrical resistance of a given copper wire using a potentiometer by comparing the potential drops across the unknown resistance and a standard (known) resistance when the same current flows through both.

Apparatus Required

  • Potentiometer (10-wire type or single-wire, length 4–10 m)
  • Copper wire specimen (unknown resistance X, mounted on a frame)
  • Standard resistance box or known resistance R (e.g., 1 Ω or 2 Ω)
  • Battery or accumulator (2 V, low internal resistance)
  • Galvanometer (sensitive, centre-zero type)
  • Jockey (sliding contact for the potentiometer wire)
  • Rheostat (to control current in the primary circuit)
  • Ammeter (0–1 A range)
  • Connecting wires (copper, insulated)
  • One-way key (for the primary circuit)
  • Two-way plug key or DPDT switch (to alternately connect X and R into the secondary circuit)

Theory & Principle

Potentiometer Principle

A potentiometer is a device used to measure potential difference accurately. It consists of a long uniform wire through which a steady current is passed from an external battery (the primary circuit). Because the wire has uniform cross-sectional area and resistivity, its resistance is distributed uniformly along its length. By Ohm’s law, when a constant current I flows through this wire, the potential drop across any segment is directly proportional to the length of that segment.

V ∝ l    (for constant current through uniform wire)
The potential drop V across a length l is proportional to l

Potential Gradient

The potential gradient is defined as the fall of potential per unit length of the potentiometer wire. If the total EMF of the driver cell produces a potential difference V across the full length L of the wire, then the potential gradient is:

k = V / L    (volt per metre)
Potential gradient — the key calibration quantity of a potentiometer

Any potential difference to be measured is balanced against an appropriate length of the potentiometer wire, where the potential drop equals k × l. At the balance point, no current flows through the galvanometer, making this a null method of measurement.

Method: Comparing Potential Drops

In this experiment, the unknown resistance X (copper wire) and a known standard resistance R are connected in series in a secondary circuit so that the same current i passes through both. Using a two-way key, we alternately connect the potentiometer’s galvanometer arm across X and across R.

When the galvanometer arm is connected across the unknown resistance X and the jockey is moved along the wire until the galvanometer reads zero, let the balance length be l₁. Then:

VX = i · X = k · l₁
Potential drop across unknown resistance X balanced at length l₁

Similarly, when the galvanometer arm is connected across the known resistance R and a new balance length l₂ is found:

VR = i · R = k · l₂
Potential drop across known resistance R balanced at length l₂

Dividing the two equations eliminates both the current i and the potential gradient k:

X / R = l₁ / l₂   ⇒   X = R × (l₁ / l₂)
Working formula — the unknown resistance X in terms of known quantities

Connection to Fundamental Laws

This experiment is rooted in two foundational principles of circuit theory:

  • Ohm’s Law (V = IR): The potential drop across each resistance is the product of the common current and that resistance. This is what allows us to write VX = iX and VR = iR.
  • Kirchhoff’s Voltage Law (KVL): Around any closed loop, the algebraic sum of EMFs and potential drops is zero. The potentiometer’s balance condition is essentially the statement that the potential drop across the segment of the potentiometer wire exactly equals the potential drop across the resistance in the secondary circuit, so the net EMF around the galvanometer loop is zero and no current flows.
Why this method is precise: At the balance point, the galvanometer draws zero current from the secondary circuit, so the measurement is free from errors due to the galvanometer’s own resistance. This null-method approach gives results more accurate than direct voltmeter readings.

Circuit Diagram

The diagram below shows the potentiometer arrangement for comparing potential drops across the unknown resistance X (copper wire) and the known resistance R.

A B scale (cm) + − E K Rh A P X (Cu wire) 2-way R (known) Q G J Jockey Primary circuit Secondary circuit l (balance length)
Diagram Key: The primary circuit (battery E, key K, rheostat Rh, ammeter A) drives a steady current through the potentiometer wire A–B. The secondary circuit has the copper wire X and known resistance R in series, with a two-way key to select which one is connected to the galvanometer G. The jockey J slides along the wire to locate the balance point.

Procedure

  1. Set up the circuit as shown in the diagram. Connect the battery E, rheostat Rh, ammeter A, and one-way key K in series across the terminals A and B of the potentiometer wire (primary circuit). Connect the copper wire specimen X and the standard resistance R in series in the secondary circuit, with a two-way plug key to switch between them. Attach the galvanometer G between the junction point and the jockey J.
  2. Check all connections carefully before closing any key. Ensure the positive terminal of the battery is connected to end A of the potentiometer wire. Verify that the galvanometer is protected by a high-resistance shunt or series resistance during initial adjustments.
  3. Close the primary key K and adjust the rheostat so that a small, steady current (read on the ammeter) flows through the potentiometer wire. The current should be small enough that the wire does not heat appreciably but large enough to give a measurable deflection of the galvanometer when the jockey is pressed at either end of the wire.
  4. Connect the unknown resistance X into the secondary circuit using the two-way key. Touch the jockey gently on the potentiometer wire near end A and note the direction of galvanometer deflection. Move the jockey toward B and find the point where deflection reverses. Carefully locate the exact point where the galvanometer shows zero deflection (the null point). Record this balance length as l₁.
  5. Switch the two-way key to connect the known resistance R in place of X (keeping the same current flowing). Again slide the jockey along the wire to locate the new balance point where the galvanometer shows zero deflection. Record this balance length as l₂.
  6. Repeat the measurements five times by slightly adjusting the rheostat to change the current each time. For every setting, find both l₁ (for X) and l₂ (for R). Tabulate all readings.
  7. Calculate X for each observation using the formula X = R × (l₁ / l₂). Find the mean value of X from all five trials.
  8. Record the value of the standard resistance R used and the least count of the measuring scale. Express the final result with appropriate significant figures and an estimate of experimental uncertainty.
Precautions:
  • Do not slide the jockey harshly along the wire; press gently and lift between trials to avoid scratching the wire and changing its cross-section.
  • Ensure the current remains steady during both measurements l₁ and l₂ for a given trial. Do not change the rheostat setting between the two readings of a single trial.
  • The EMF of the driver battery must be greater than the potential drop across either X or R to ensure a balance point exists on the wire.
  • Keep connections tight and clean to avoid contact resistance. Sand the wire ends and binding posts if necessary.
  • Allow the circuit to settle for a few seconds after closing the key before taking readings, to avoid transient effects.
  • Read the balance length by keeping the eye directly above the jockey to avoid parallax error.

Observation Table

Standard resistance used: R = 1.00 Ω

Least count of scale: 0.1 cm

S.No. Balance length for X, l₁ (cm) Balance length for R, l₂ (cm) X = R × l₁/l₂ (Ω)
1 162.5 250.0 0.650
2 158.3 245.2 0.646
3 170.0 260.8 0.652
4 155.7 238.0 0.654
5 165.4 253.6 0.652

Calculations

Sample Calculation (Observation 1):

Given: R = 1.00 Ω, l₁ = 162.5 cm, l₂ = 250.0 cm

X = R × (l₁ / l₂)

X = 1.00 × (162.5 / 250.0)

X = 1.00 × 0.650

X = 0.650 Ω

Mean Value:

Xmean = (0.650 + 0.646 + 0.652 + 0.654 + 0.652) / 5

Xmean = 3.254 / 5

Xmean = 0.651 Ω

Uncertainty Estimate:

Maximum deviation from mean = |0.651 − 0.646| = 0.005 Ω

A conservative uncertainty of ±0.03 Ω accounts for both random scatter and systematic effects (scale reading, contact resistance).

Result

The electrical resistance of the given copper wire specimen is:

X = 0.65 ± 0.03 Ω

This value was obtained using a potentiometer with a 1.00 Ω standard resistance by the method of comparing potential drops. The null-method measurement ensures that the result is free from errors arising due to galvanometer resistance.

Sources of Error

  1. Non-uniform potentiometer wire: If the wire does not have a perfectly uniform cross-sectional area throughout its length, the resistance per unit length varies, violating the fundamental assumption that the potential drop is proportional to length. This introduces a systematic error in all balance-length readings.
  2. Thermo-EMF at junctions: When dissimilar metals come in contact (e.g., copper connecting wire and the alloy potentiometer wire), small thermo-electric EMFs are generated due to temperature differences at the junctions. These stray EMFs add to or subtract from the potential being measured, producing a false null point.
  3. Fluctuating current in the primary circuit: If the battery EMF drifts or the rheostat contact is unstable, the current through the potentiometer wire changes between the measurements of l₁ and l₂. Since the method relies on the same potential gradient for both readings, any current variation directly affects the ratio and hence the calculated resistance.
  4. Loose or dirty connections: High contact resistance at any terminal introduces unwanted voltage drops that are not accounted for in the theoretical formula. Oxidized or loosely clamped connections are a frequent cause of irreproducible readings.
  5. Parallax error in reading the scale: If the eye is not positioned directly above the point where the jockey touches the wire, the balance length is read incorrectly. This random error can be minimized by using a magnifying glass and reading the scale perpendicularly.

Viva Voce Questions

A potentiometer works on the principle that when a constant current flows through a wire of uniform cross-section and composition, the potential drop across any length of the wire is directly proportional to that length. Mathematically, V = kl, where k is the potential gradient (potential drop per unit length) and l is the length of the wire segment.

This proportionality holds because a uniform wire has uniform resistance per unit length. By Ohm’s law, V = IR, and since R itself is proportional to length (R = ρl/A for uniform ρ and A), the potential drop is proportional to length when the current is constant.

The potentiometer is classified as a null instrument because at the balance point, no current is drawn from the circuit under test. This gives it theoretically infinite input impedance at balance, making it more accurate than a voltmeter for precision measurements.

The potential gradient of a potentiometer wire is the fall of potential (voltage drop) per unit length of the wire. It is denoted by k and expressed in volts per metre (V/m) or volts per centimetre (V/cm).

If the total potential difference across the full length L of the potentiometer wire is V, then:

k = V / L

The potential gradient can be adjusted by changing the current through the wire (using the rheostat) or by changing the total length of wire in use. A smaller potential gradient makes the potentiometer more sensitive, because a given potential difference corresponds to a longer balance length, allowing more precise location of the null point.

In practice, the potential gradient can be determined by balancing a known EMF (such as a standard cell) against a measured length of the wire. If a standard cell of EMF Es balances at length ls, then k = Es / ls.

A potentiometer is preferred over a voltmeter for measuring electromotive force (EMF) for the following reasons:

  • Zero current at balance: At the null point, the potentiometer draws no current from the source whose EMF is being measured. This means there is no voltage drop across the internal resistance of the source, so the true EMF is measured. A voltmeter, by contrast, always draws some current (however small), causing an internal voltage drop and giving a reading of terminal voltage, which is lower than the actual EMF.
  • Infinite effective resistance: Since no current flows at balance, the potentiometer behaves as though it has infinite resistance, whereas a voltmeter has finite (though often high) resistance.
  • Higher accuracy: The null method is inherently more precise than a deflection method because the final reading depends on a length measurement rather than on the calibration accuracy of a meter movement.

The potentiometer essentially compares an unknown potential difference against a known, calibrated reference, making it a fundamental standard for voltage measurement.

Both the potentiometer and the Wheatstone bridge are null-method instruments that use a galvanometer to detect the balance condition (zero current through the galvanometer arm).

In a Wheatstone bridge, four resistances P, Q, R, and S are arranged in a diamond, and at balance: P/Q = R/S. The unknown resistance is found by comparison with known resistances.

In this potentiometer experiment, we effectively compare two potential drops using lengths of a uniform wire. At balance: X/R = l₁/l₂. The ratio of balance lengths plays the same role as the ratio of bridge arms.

The potentiometer can be thought of as a linear (stretched-out) form of the Wheatstone bridge, where the two arms formed by the potentiometer wire segments (of lengths l₁ and L − l₁, or l₂ and L − l₂) replace two of the four bridge arms. Both instruments exploit the proportionality of potential drops to resistances when the same current flows through them.

A practical difference is that the potentiometer offers continuously variable comparison (by sliding the jockey) rather than discrete steps (by switching resistance boxes), which can give finer resolution.

The rheostat in the primary circuit of the potentiometer serves two important purposes:

  • Current control: By varying the resistance of the rheostat, the current flowing through the potentiometer wire can be increased or decreased. This directly controls the potential gradient (k = V/L) along the wire. A suitable current must be chosen so that the balance points fall at convenient, well-separated positions on the wire.
  • Ensuring a balance point exists: The total potential drop across the potentiometer wire must be greater than the potential drop across the resistance being measured. If the current is too low, the potential gradient may be so small that the required balance length exceeds the total wire length, and no null point can be found. Conversely, if the current is too high, the balance point may be very close to end A, reducing measurement precision. The rheostat allows fine adjustment to place the balance point near the middle of the wire, where the percentage error in length measurement is smallest.

Additionally, the rheostat protects the potentiometer wire and the battery from excessive current, preventing overheating and ensuring stable operation throughout the experiment.

← Back to All Experiments