Measure EMF and Internal Resistance of a Cell Using Potentiometer
✅ FREE Experiment • 🔬 Interactive Circuit • 🎓 NEB Class 12 Physics
A potentiometer is a versatile instrument used to measure potential difference (voltage) without drawing any current from the circuit. This makes it ideal for accurately measuring the EMF (electromotive force) and internal resistance of cells. Unlike a voltmeter, which draws some current, the potentiometer operates on the null deflection method - finding a balance point where no current flows through the galvanometer.
In this experiment, you'll use a potentiometer wire to find balancing points for a cell in both open circuit (EMF measurement) and closed circuit (terminal voltage measurement) conditions. From these measurements, you can calculate the cell's internal resistance using the formula: r = (E - V)/V × R.
Given: EMF of driver cell = 2.0 V, Length of potentiometer wire = 100 cm
| S.No. | Open Circuit (EMF) | Closed Circuit (Terminal V) | Internal Resistance r = (E - V)/V × R (Ω) |
||
|---|---|---|---|---|---|
| Length L₁ (cm) | EMF E = kL₁ (V) | Length L₂ (cm) | Voltage V = kL₂ (V) | ||
| No observations recorded yet. Click "Record" to add readings | |||||
Mean Internal Resistance: Calculate after recording observations
A potentiometer is a device used to measure potential difference (voltage) and compare EMFs of different cells. It consists of a long uniform wire (usually 10m, coiled) stretched along a meter scale, with a driver cell maintaining constant current through it.
When a constant current flows through a uniform wire, the potential drop across any length of the wire is directly proportional to that length. If the potential gradient (voltage per unit length) is k V/cm, then:
Where V is voltage, k is potential gradient, and L is length along the wire.
The potentiometer works on the principle of null deflection. When the potential difference across the potentiometer wire between two points equals the EMF of the test cell, no current flows through the galvanometer. This point is called the balancing point, and the corresponding length is the balancing length.
When the cell is in open circuit (no current drawn), the jockey is moved along the wire until the galvanometer shows zero deflection. At this balancing point:
Where E is EMF, k is potential gradient, and L₁ is balancing length.
When a resistance R is connected across the cell, current flows and the terminal voltage V (which is less than EMF) is measured by finding new balancing length L₂:
The relationship between EMF (E), terminal voltage (V), current (I), and internal resistance (r) is:
Rearranging to solve for internal resistance r:
Since E = kL₁ and V = kL₂, we can also write:
The potential drop per unit length of the potentiometer wire. If driver EMF is E₀ and wire length is L:
At balance point, potential difference across wire segment = cell EMF/voltage:
The potentiometer works on the principle that when a constant current flows through a uniform wire, the potential drop is directly proportional to the length of the wire. At the balancing point, the potential difference across a segment of wire equals the EMF being measured, causing zero current through the galvanometer.
Because the potentiometer uses null deflection method - at balance, no current flows through the galvanometer, so no current is drawn from the cell. A voltmeter always draws some current, which causes potential drop across internal resistance, so it measures terminal voltage, not true EMF. Potentiometer measures actual EMF with high accuracy.
Balancing length is the length of potentiometer wire from the zero end to the point where the galvanometer shows zero deflection. At this point, the potential difference across this length of wire exactly equals the EMF or voltage being measured.
The driver cell creates potential difference across the entire potentiometer wire. If test cell EMF is greater than driver cell EMF, the balancing point will lie beyond the wire length, making measurement impossible. Driver EMF must exceed test EMF to ensure balancing point falls on the wire.
Potential gradient (k) is the potential drop per unit length of the potentiometer wire. It's calculated as: k = (Driver cell EMF) / (Total wire length). Units are V/cm or V/m. If driver EMF is 2V and wire length is 100 cm, then k = 2/100 = 0.02 V/cm.
Internal resistance is the resistance offered by the electrolyte and electrodes inside the cell to the flow of current. When current flows, there's a potential drop (Ir) across this internal resistance, making terminal voltage less than EMF: V = E - Ir. Good cells have low internal resistance.
Starting from Ohm's law for a cell:
E = V + Ir (where I is current)
Current I = V/R (from external circuit)
Substituting: E = V + (V/R) × r
E = V(1 + r/R)
E/V = 1 + r/R
E/V - 1 = r/R
(E - V)/V = r/R
Therefore: r = (E - V)/V × R
L₁ corresponds to EMF (E) in open circuit, while L₂ corresponds to terminal voltage (V) in closed circuit. When current flows (closed circuit), potential drop occurs across internal resistance, so V = E - Ir, meaning V < E. Since V = kL, smaller voltage means smaller balancing length. Therefore L₂ < L₁.
The galvanometer is a sensitive current detector used to indicate the null point. When there's a potential difference between wire and cell, current flows through galvanometer causing deflection. At balancing point, potentials are equal, no current flows, and galvanometer shows zero deflection - this is how we detect the balance.
No! The driver cell must always have higher EMF than the test cell. The driver cell maintains current through the potentiometer wire, creating the potential gradient. The test cell EMF must be less so its balancing point falls within the wire length. If reversed, measurement is impossible.
A longer wire gives: (1) Smaller potential gradient (k = E/L), making measurements more precise, (2) Greater balancing lengths, reducing percentage error in length measurement, (3) Better resolution for small voltage differences. For example, 10m wire gives 10 times better resolution than 1m wire.
The wire must be uniform (constant cross-sectional area and resistivity) so that resistance per unit length is constant. This ensures potential drop is directly proportional to length (V ∝ L). If wire is non-uniform, this relationship breaks down and accurate measurements are impossible.
Pressing too hard can: (1) Damage the wire coating or create grooves, making it non-uniform, (2) Create better contact temporarily but damage wire permanently, (3) Change wire's resistance at that point. Gentle, consistent pressure is necessary for accurate, repeatable measurements.
Not directly, but it can measure current indirectly. If we pass the current through a known resistance (R) and use potentiometer to measure voltage (V) across it, then current can be calculated using Ohm's law: I = V/R. This method is more accurate than using an ammeter for small currents.
Sensitivity is the smallest potential difference the potentiometer can measure. It depends on: (1) Potential gradient k (smaller k = higher sensitivity), (2) Galvanometer sensitivity (detects smaller currents), (3) Wire length (longer = more sensitive). A sensitive potentiometer can measure potential differences as small as microvolts.