DETERMINATION OF INTERNAL RESISTANCE OF A PRIMARY CELL

To determine the internal resistance of a given primary cell using a potentiometer.

• Potentiometer wire (1-2 meters long)
• Leclanche cell (test cell whose internal resistance is to be determined)
• Standard cell (e.g., Weston cell or another cell with known EMF)
• Galvanometer
• Resistance box (0-100 Ω)
• One-way key
• Two-way key
• Jockey (contact maker)
• Connecting wires
• Ammeter (0-3 A)
• Rheostat
• Battery or power supply (4-6 V)

The potentiometer works on the principle that when a constant current flows through a wire of uniform cross-section, the potential difference between any two points on the wire is directly proportional to the length of the wire between those points.

According to Ohm's law, if a current $I$ flows through a resistance $R$, the potential difference $V$ across it is:

In a potentiometer setup, when a cell of EMF $E$ is balanced against a length $l$ of the potentiometer wire, we have:

The internal resistance of a cell is the resistance offered by the cell itself to the flow of current through it. When a current is drawn from a cell, its terminal potential difference $(V)$ is less than its EMF $(E)$ due to the voltage drop across the internal resistance $(r)$:

Where:

• $E$ is the EMF of the cell
• $I$ is the current drawn from the cell
• $r$ is the internal resistance of the cell
• $V$ is the terminal potential difference

In this experiment, we use the potentiometer to measure:

1. The EMF $(E)$ of the test cell when no current is drawn (open circuit)
2. The terminal potential difference $(V)$ when a current is drawn through a known external resistance

From these measurements, we can calculate the internal resistance of the cell.

The internal resistance $(r)$ of the primary cell can be calculated using the formula:

Where:

• $r$ is the internal resistance of the cell
• $R$ is the external resistance connected to the cell
• $E_1$ is the EMF of the cell (measured when no current is drawn)
• $V$ is the terminal potential difference of the cell when current is drawn through resistance $R$

Alternatively, if $l_1$ is the balancing length for EMF and $l_2$ is the balancing length for terminal potential difference, then:

Where $l_1$ and $l_2$ are the balancing lengths on the potentiometer wire.

1. Setup the circuit:
   • Connect the primary circuit as shown in the diagram, consisting of a battery, rheostat, ammeter, and potentiometer wire.
   • Connect the secondary circuit with the galvanometer, jockey, and two-way key K₂.
2. Standardize the potentiometer:
   • Close the primary circuit using key K₁.
   • Adjust the rheostat to ensure sufficient current flows through the potentiometer wire.
   • Connect the standard cell E₂ to the circuit using the two-way key K₂.
   • Move the jockey along the wire until the galvanometer shows zero deflection. Note this position as the balancing length for the standard cell.
3. Measure the EMF of the test cell:
   • Switch the two-way key K₂ to connect the test cell E₁ (without any external resistance).
   • Find the balancing point by moving the jockey and note this length as $l_1$.
4. Measure the terminal potential difference:
   • Connect a suitable resistance $R$ from the resistance box in series with the test cell.
   • Find the new balancing point and note this length as $l_2$.
   • Repeat this step with at least 5 different values of $R$.
5. Calculate the internal resistance:
   • For each set of readings, calculate the internal resistance using the formula: $r = R(l_1/l_2 - 1)$
   • Take the mean value of all calculated internal resistances.

Table 1: Standardization of Potentiometer

S.No.	Standard Cell EMF (V)	Balancing Length (cm)	Potentiometer Sensitivity (V/cm)
1

Table 2: Determination of Internal Resistance

S.No.	External Resistance R (Ω)	Balancing Length for EMF $l_1$ (cm)	Balancing Length for Terminal PD $l_2$ (cm)	Internal Resistance $r = R(l_1/l_2 - 1)$ (Ω)
1
2
3
4
5

1. Calculate the potentiometer sensitivity:
   Sensitivity = \frac{\text{EMF of standard cell}}{\text{Balancing length for standard cell}}
2. For each set of readings, calculate the EMF ($E_1$) and terminal potential difference (V) of the test cell:
   E_1 = \text{Sensitivity} \times l_1
   V = \text{Sensitivity} \times l_2
3. Calculate the internal resistance for each reading using:
   r = R\left(\frac{E_1}{V} - 1\right) \text{ or } r = R\left(\frac{l_1}{l_2} - 1\right)
4. Calculate the mean value of the internal resistance:
   r_{mean} = \frac{r_1 + r_2 + r_3 + r_4 + r_5}{5}
5. Calculate the percentage error (if an accepted value is available):
   \% \text{Error} = \frac{|r_{mean} - r_{accepted}|}{r_{accepted}} \times 100

The internal resistance of the given primary cell is _____ Ω ± _____ Ω.

1. The potentiometer wire should be of uniform cross-section and free from kinks.
2. The connections should be tight and clean to avoid contact resistance.
3. The jockey should touch the wire gently to avoid damage to the wire.
4. The resistances used should be accurate and in good condition.
5. The galvanometer should be sensitive enough to detect small changes in current.
6. The battery used in the primary circuit should provide a steady current.
7. The rheostat should be adjusted to maintain sufficient current in the potentiometer wire.
8. Avoid parallax error while taking readings on the potentiometer scale.
9. The room temperature should be noted as EMF varies slightly with temperature.
10. The keys should be pressed only when readings are being taken to avoid unnecessary current drain.

1. Non-uniformity in the cross-section of the potentiometer wire.
2. Temperature variations during the experiment affecting the resistance of the wire.
3. Contact resistance at junctions and connections.
4. Thermo-electric EMF generated at junctions of dissimilar metals.
5. Parallax error in reading the position of the jockey.
6. Fluctuations in the primary circuit current.
7. Zero error in the galvanometer.
8. Error in the resistance box values.
9. Polarization effects in the cell during the experiment.
10. Improper standardization of the potentiometer.