1 Aim

To determine and compare the electromotive forces (EMFs) of two given primary cells using a potentiometer.

2 Apparatus Used

• Potentiometer wire (typically 10 meters long)
• Wooden board with scale
• Two primary cells (e.g., Daniel cell, Leclanche cell)
• Standard cell (e.g., Weston cell) with known EMF
• Galvanometer
• Jockey (sliding contact)
• One-way key
• Two-way key
• Rheostat (variable resistance)
• Battery or power supply (2V)
• Connecting wires
• Sandpaper (for cleaning contacts)

3 Diagram

4 Theory

The potentiometer works on the principle that when a steady 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.

When a primary cell is connected to the potentiometer wire through a galvanometer and a jockey, there exists a point on the wire where the potential difference across that length of wire exactly balances the EMF of the cell. At this null point, no current flows through the galvanometer.

Therefore, the ratio of EMFs is equal to the ratio of balancing lengths:

If one of the cells is a standard cell with known EMF ($E_s$), then the EMF of the other cell ($E_x$) can be calculated as:

5 Formula

Where:

• $E_1, E_2$: EMFs of the two cells
• $l_1, l_2$: Corresponding balancing lengths
• $E_s$: EMF of standard cell
• $l_s$: Balancing length for standard cell
• $E_x$: EMF of unknown cell
• $l_x$: Balancing length for unknown cell

6 Procedure

1. Set up the apparatus:
   • Mount the potentiometer wire on the wooden board.
   • Connect the driver battery, rheostat, and one-way key K₁ in series with the potentiometer wire.
   • Connect the galvanometer in series with the two-way key K₂.
2. For the first primary cell:
   • Connect the first cell ($E_1$) to one terminal of the two-way key K₂.
   • Close the key K₁ to allow current through the potentiometer wire.
   • Set the two-way key K₂ to connect the first cell to the circuit.
   • Place the jockey at one end of the potentiometer wire and note the deflection in the galvanometer.
   • Move the jockey to the other end and verify that the galvanometer deflects in the opposite direction.
   • Find the null point by moving the jockey along the wire until the galvanometer shows zero deflection.
   • Record the position ($l_1$) of the jockey at this null point.
   • Repeat the process 3-5 times and calculate the average value of $l_1$.
3. For the second primary cell:
   • Connect the second cell ($E_2$) to the other terminal of the two-way key K₂.
   • Set the two-way key K₂ to connect the second cell to the circuit.
   • Repeat the process of finding the null point as done for the first cell.
   • Record the position ($l_2$) of the jockey at this null point.
   • Repeat the process 3-5 times and calculate the average value of $l_2$.
4. Calculate the ratio of EMFs using the formula $\frac{E_1}{E_2} = \frac{l_1}{l_2}$.
5. For absolute value measurement:
   • If one of the cells is a standard cell with known EMF, calculate the EMF of the other cell.

7 Observation Table

Table 1: Balancing Length for First Cell ($E_1$)

Observation No.	Balancing Length $l_1$ (cm)
1
2
3
4
5
Mean

Table 2: Balancing Length for Second Cell ($E_2$)

Observation No.	Balancing Length $l_2$ (cm)
1
2
3
4
5
Mean

8 Calculations

1. Calculate the mean balancing length for cell 1 ($E_1$):

   Mean $l_1$ = $\frac{\text{Sum of all }l_1\text{ readings}}{\text{Number of readings}}$

2. Calculate the mean balancing length for cell 2 ($E_2$):

   Mean $l_2$ = $\frac{\text{Sum of all }l_2\text{ readings}}{\text{Number of readings}}$

3. Calculate the ratio of EMFs:

   $\frac{E_1}{E_2} = \frac{\text{Mean }l_1}{\text{Mean }l_2}$

4. If cell 1 is a standard cell with known EMF ($E_s$), calculate the EMF of cell 2:

   $E_2 = E_1 \times \frac{\text{Mean }l_2}{\text{Mean }l_1}$

9 Result

1. The balancing length for the first cell ($E_1$) is _____ cm.
2. The balancing length for the second cell ($E_2$) is _____ cm.
3. The ratio of EMFs ($\frac{E_1}{E_2}$) is _____.
4. The EMF of cell 1 is _____ volts.
5. The EMF of cell 2 is _____ volts.

10 Precautions

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 make a gentle contact with the wire to avoid damage.
4. The current through the potentiometer wire should remain constant throughout the experiment.
5. The galvanometer should be sensitive enough to detect small currents.
6. The primary cells should be in good condition with stable EMFs.
7. Avoid parallax error while taking readings on the scale.
8. The driver battery should have much higher EMF than the cells being measured.
9. The rheostat should be adjusted to ensure the potentiometer is properly calibrated.
10. Avoid heating effects by not keeping the circuit closed for extended periods.

11 Sources of Error

1. Non-uniform cross-section of the potentiometer wire.
2. Temperature variations causing resistance changes in the wire.
3. Poor contact between the jockey and the wire.
4. Internal resistance of the cells affecting measurements.
5. Thermoelectric effects at junctions of different metals.
6. Polarization of cells during the experiment.
7. Fluctuations in the driver battery voltage.
8. Parallax errors in reading the scale.
9. Galvanometer zero error or insufficient sensitivity.
10. Contact resistance at terminals and connections.

12 Viva Voice Questions