Potentiometer

Think of it like a tug-of-war rope where one side is a known, adjustable "pull" (potential drop along the wire) and the other side is the unknown cell's EMF. You slide the point of contact until neither side wins — that balance point tells you the unknown value, similar to how Khan Academy frames it as sliding a contact until the "vote" (galvanometer) shows zero.

A potentiometer is an instrument used to measure the EMF of a cell, compare EMFs of two cells, or find a cell's internal resistance — all without drawing any current from the cell being measured, making it more accurate than a voltmeter.

The potential drop across any length of a uniform wire is directly proportional to that length, provided a constant current flows through it.

where K is the potential gradient (potential drop per unit length, in V/m), and l is the length of wire from the starting point A.

At the null point, the unknown EMF exactly equals the potential drop across the balancing length:

1. A driving battery B₁​ sends a steady current through the long potentiometer wire AB, creating a uniform potential drop from A to B.
2. The unknown cell E is connected with its positive terminal at A and its negative terminal through a galvanometer to a sliding jockey J.
3. As the jockey moves along the wire, it compares the wire's potential (at that point) with the cell's EMF.
4. If the jockey touches a point where the wire's potential is lower than E, current from the cell dominates — the galvanometer deflects one way.
5. If the wire's potential is higher than E, the battery's current dominates — the galvanometer deflects the other way.
6. Somewhere in between is the null point, where the galvanometer shows zero deflection — at this point, no current flows through the cell, so the wire's potential drop exactly equals the cell's EMF.

Calibrating the Wire (Finding K)

Replace the unknown cell with a standard Weston cadmium cell (EMF = 1.0184 V), find its null point at length l′, and calculate:

A potentiometer is more sensitive when even a slight jockey movement away from the null point causes a large galvanometer deflection. Sensitivity improves as the potential gradient K decreases — achieved by using a longer wire.

Construction

• Wire material: constantan or manganin (high resistivity, low temperature coefficient)
• Length: typically 4–12 m, laid out as 1 m segments on a wooden board, connected by thick copper strips
• A meter scale runs parallel to the wire for reading jockey position

Connect both cells (positive terminals to A) via a two-way key, and find their null points l₁​ and l₂:

Because no current flows at the null point, the internal resistance of the cells does not affect the result — this is the key reason potentiometers beat voltmeters for this measurement.

1. With the resistance-box key open, find null point l₁ → gives EMF: E = Kl₁
2. Close the key, insert resistance R, find new null point l₂ → gives terminal PD: V = Kl₂
3. Internal resistance: r = R(\[\frac {l_1}{l_2}\] − 1)

• Connect positive terminals of all cells to the same end (A).
• Driver battery EMF must exceed every test cell's EMF, or no null point will form.
• Wire must have uniform cross-section throughout.
• Avoid prolonged current flow (heating changes resistance and gradient).
• Use a shunt with the galvanometer initially; remove it only near the null point for fine adjustment.
• Never rub the jockey along the wire — this damages uniformity.

A 10 m potentiometer wire balances a 1.018 V standard cell at 850 cm.

• Potential gradient: K = 1.018/850 = 1.2 × 10⁻³ V/cm
• Maximum measurable EMF = K × total length = 1.2 × 10⁻³ × 1000 = 1.2 V

A 10 m wire (20 Ω) in series with 480 Ω and a 5 V battery balances an unknown EMF at 6 m.

• Current: I = 5/500 = 0.01 A
• V_AB = 0.01 × 20 = 0.2 V, so K = 0.2/10 = 0.02 V/m
• e = K × l = 0.02 × 6 = 0.12 V

• l₁ = 76.3 cm, l₂ = 64.8 cm, R = 9.5 Ω
• r = (\[\frac {76.3}{64.8}\] − 1) × 9.5 = 1.7 Ω

• Potentiometer principle: V ∝ l for a uniform wire carrying constant current.
• At the null point, no current flows through the test cell — giving the true EMF, not just terminal voltage.
• Sensitivity increases with a longer wire (lower potential gradient).
• Three major uses: measuring EMF, comparing two EMFs, and finding internal resistance.
• A potentiometer behaves like an ideal (infinite-resistance) voltmeter, making it more accurate than a real voltmeter.