Imagine trying to measure a person’s weight by placing your hand on their shoulder — just your touch changes how they stand. That’s exactly the problem with using a voltmeter to measure EMF: every voltmeter draws some current, which creates a voltage drop across the cell’s internal resistance, making the reading slightly lower than the true EMF. The potentiometer was invented to solve this exact problem: it measures voltage by balancing it against a known reference, drawing zero current at the point of measurement.
The potentiometer is one of the most elegant instruments in electrical physics. It appears simple — just a long resistance wire on a board, a battery, and a galvanometer — but it can measure EMF with extraordinary accuracy, compare the EMFs of two cells, and determine the internal resistance of a battery. It is a mandatory instrument in the CBSE Class 12 Physics practical syllabus (Chapter 3: Current Electricity) with two standard experiments that are examined in board practicals.
This guide covers the potentiometer completely: its definition, the principle of operation, construction and parts, working explanation, the two CBSE experiments (comparing EMF and finding internal resistance) with step-by-step procedures and derivations, the key advantages over a voltmeter, types, and uses. All potentiometer apparatus described is manufactured and supplied by AJKANT Overseas from Ambala, India.
- 1. What is a Potentiometer?
- 2. Principle of the Potentiometer
- 3. Construction and Parts
- 4. How a Potentiometer Works
- 5. Experiment 1 — Compare EMF of Two Cells
- 6. Experiment 2 — Find Internal Resistance of a Cell
- 7. Potentiometer vs Voltmeter
- 8. Uses of Potentiometer
- 9. Frequently Asked Questions (FAQ)
1. What is a Potentiometer?
A potentiometer is an electrical instrument used to measure potential differences (voltages) accurately by comparing an unknown EMF or voltage against a known, calibrated reference voltage — at the condition of zero current flow (null condition). Because no current flows from the source being measured at the balance point, the potentiometer does not disturb the circuit and measures the true EMF, unlike a voltmeter which always draws some current.
In a school physics lab, the potentiometer consists of:
- A long, uniform resistance wire (usually 1 metre per section, arranged over 4–10 sections on a wooden board)
- A driver cell (battery/accumulator) that maintains a steady, uniform current through the wire
- A jockey (sliding contact) that can touch any point on the wire
- A galvanometer as the null detector
- The unknown EMF source (cell) being measured
2. Principle of the Potentiometer
The working of a potentiometer rests on a simple, powerful principle derived from Ohm’s Law and the properties of a uniform resistance wire.
Consider a uniform wire of length L, resistance R, and cross-sectional area A, through which a current I flows from a driver cell. By Ohm’s Law, the potential difference across the entire wire is V = IR. For any small portion of length l, its resistance is (R/L) × l, so the potential difference across it is:
φ = V/L = IR/L (Volts per metre)
For any length l: V = φ × l
At the null (balance) point: the unknown EMF exactly equals the potential difference across the wire length lᵇ:
E = φ × lᵇ ⇒ E = (V/L) × lᵇ
3. Construction and Parts
4. How a Potentiometer Works
The working of the potentiometer is based on finding the null (balance) point — the position of the jockey on the wire where the galvanometer reads exactly zero.
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Establish Potential GradientThe driver cell is connected across the full length of the potentiometer wire (through a rheostat). This drives a steady current through the wire, establishing a uniform potential gradient φ = V/L volts/metre from one end (higher potential) to the other end (lower potential). Every point on the wire has a definite, fixed potential relative to the low-potential end.
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Connect Unknown CellThe unknown cell (EMF = E) is connected with its positive terminal to the same high-potential end of the wire as the driver cell’s positive terminal. The negative terminal of the cell connects through the galvanometer to the jockey. This creates a situation where the cell’s EMF is competing against the wire’s potential at the jockey’s contact point.
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Slide Jockey to Find Null PointThe jockey is pressed onto the wire and slid along its length. At most positions, either the cell’s EMF exceeds the wire potential (galvanometer deflects one way) or the wire potential exceeds the cell’s EMF (galvanometer deflects the other way). At one specific length lᵇ, the potential of the wire exactly equals the cell’s EMF — no current flows through the galvanometer (null deflection). This is the balance point.
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Read Balance Length and CalculateThe balance length lᵇ is read from the mm scale on the board. Then: E = φ × lᵇ. Since the galvanometer reads zero, no current is drawn from the unknown cell at this moment — so the measured voltage is the true EMF of the cell, not the terminal voltage (which would be reduced by I × r, where r is internal resistance).
5. Experiment 1 — Comparing EMF of Two Cells
Circuit Setup: The driver cell (accumulator) is connected across the full wire. Cell 1 (EMF E₁) is connected to the circuit through key K₁. Cell 2 (EMF E₂) is connected through key K₂. Only one cell is in the circuit at a time. The galvanometer connects from the jockey to the common negative terminal of both cells.
Procedure:
- Close K₁ (connect Cell 1). Find the balance length l₁ (galvanometer reads zero). Record l₁.
- Open K₁, close K₂ (connect Cell 2). Find the balance length l₂. Record l₂.
- Repeat both measurements three times. Take mean values of l₁ and l₂.
- Calculate the ratio E₁/E₂ = l₁/l₂.
At balance with Cell 2: E₂ = φ × l₂
Dividing: E₁ / E₂ = l₁ / l₂
(The potential gradient φ cancels since the driver cell and rheostat setting are unchanged between the two readings.)
Observation Table format:
| Reading | Balance length for E₁ (l₁ cm) | Balance length for E₂ (l₂ cm) | E₁/E₂ = l₁/l₂ |
| 1 | | | |
| 2 | | | |
| 3 | | | |
| Mean | | | |
Result: E₁/E₂ = l₁ (mean) / l₂ (mean) = _____ (numerical ratio)
6. Experiment 2 — Finding Internal Resistance of a Cell
Theory: When no current flows from the cell (open circuit), the potentiometer measures the true EMF (E). When a resistance R is connected across the cell’s terminals, current flows through R, and the cell’s terminal voltage drops to V = E × R/(R+r), where r is the internal resistance. The potentiometer measures V (terminal voltage) in this case. From E and V, we can find r.
Procedure:
- With key K₂ open (R not connected): Find balance length l₁ = balance length for EMF (E). Record.
- Close K₂ (connect R across the cell terminals). The cell now delivers current through R. Find new balance length l₂ = balance length for terminal voltage (V). Record.
- Repeat for 4–5 different values of R from the resistance box.
- For each R, calculate r using the formula below.
E = φ l₁ and V = φ l₂
Dividing: E/V = l₁/l₂
Also: E/V = (R + r)/R
Therefore: (R + r)/R = l₁/l₂
⇒ r/R = (l₁ − l₂)/l₂
⇒ r = R(l₁ − l₂)/l₂
Observation Table format:
| R (Ω) | l₁ (cm) | l₂ (cm) | r = R(l₁−l₂)/l₂ (Ω) |
| 1 | | | |
| 2 | | | |
| 3 | | | |
| Mean r = _____ Ω |
Result: Internal resistance of the given cell = r = _____ Ω
7. Potentiometer vs Voltmeter — Key Differences
| Property | Potentiometer | Voltmeter |
|---|---|---|
| Measurement principle | Null method (zero current at balance) | Deflection method (current always flows) |
| Current drawn from source | Zero at the balance point | Always draws some current (limited by high internal resistance) |
| Measures | True EMF (because no current drawn, no I.r drop) | Terminal voltage (slightly less than EMF due to I.r drop) |
| Accuracy | Very high — limited only by sensitivity of galvanometer | Moderate — limited by internal resistance of voltmeter |
| Sensitivity | Can detect very small differences in potential | Limited by scale division and internal resistance |
| Internal resistance required | Not applicable (null method) | Must be very high to minimise current drawn |
| Can measure internal resistance? | Yes (using the two-reading method) | No (cannot distinguish EMF from terminal voltage) |
| Portability | Requires a separate driver circuit — not portable | Compact, self-contained, portable |
| Use in practicals | Comparing EMF, finding internal resistance, calibrating other instruments | Quick measurement of voltages in circuits |
8. Uses of Potentiometer
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9. Frequently Asked Questions (FAQ)
The principle of a potentiometer is: “When a steady current flows through a uniform wire of uniform cross-section, the potential difference across any length of the wire is directly proportional to that length.” Mathematically: V ∝ l, so V = φl, where φ = V/L is the potential gradient (volts per metre). This means if a uniform wire of length L has a potential difference V across it, then any portion of length l has a potential difference V×(l/L) across it. The potentiometer uses this principle to compare an unknown EMF with the known potential of a calibrated wire segment.
A potentiometer is preferred over a voltmeter for measuring EMF because: (1) Zero current at balance: At the null point, no current flows from the cell being measured. This means there is no voltage drop across the cell’s internal resistance (V = E − Ir = E − 0 = E), so the true EMF is measured. A voltmeter always draws some current, causing V = E − Ir to be slightly less than E. (2) Can measure internal resistance: By measuring balance lengths under open-circuit and loaded conditions, the potentiometer can calculate internal resistance. A voltmeter cannot do this. (3) Higher accuracy: The accuracy of the potentiometer is limited only by the sensitivity of the galvanometer and the uniformity of the wire.
The formula for comparing EMFs E₁ and E₂ of two cells using a potentiometer is: E₁/E₂ = l₁/l₂, where l₁ is the balance length for Cell 1 and l₂ is the balance length for Cell 2. This formula comes from the fact that at balance: E₁ = φl₁ and E₂ = φl₂. Since the potential gradient φ is the same for both measurements (driver cell and rheostat setting unchanged), dividing gives E₁/E₂ = l₁/l₂. The measurement must be taken with the same driver cell and same rheostat position for both cells.
The formula for finding the internal resistance r of a cell using a potentiometer is: r = R(l₁ − l₂)/l₂, where R is the external resistance connected across the cell, l₁ is the balance length under open-circuit conditions (measures EMF = E), and l₂ is the balance length when R is connected (measures terminal voltage = V). Derivation: E/V = l₁/l₂ (from potentiometer principle) and E/V = (R+r)/R (from circuit analysis). Equating: (R+r)/R = l₁/l₂, which gives r = R(l₁−l₂)/l₂. Different values of R give different values of r; the mean is taken.
The EMF of the driver cell must be greater than the EMF of the cell being measured because: the potentiometer works by finding a point on the wire where the potential equals the unknown EMF. The maximum potential at any point on the wire is equal to the EMF of the driver cell (at the far end of the wire). If the unknown EMF is greater than the driver EMF, the unknown cell’s potential exceeds the potential at every point on the wire, and the galvanometer will always deflect in the same direction no matter where the jockey is placed — no null point can be found. The balance condition (E = φl) requires l to be a positive, measurable length within the wire, which is only possible when Eᵈᵅᵢᵗᵃᵅ > Eₓₓₖₓₙₓ.
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