Measurement of Internal Resistance of a Cell

Potentiometer

A potentiometer is an instrument used to measure the internal resistance of a cell by balancing it against the potential difference produced by passing a known current through a known variable resistance. The potential meter is an adjustable voltage divider formed by a three-terminal resistor with sliding or rotating contact. To change the potential meter to a variable resistor or use only two terminals, one end and the wiper. Electronic devices such as volume control on audio equipment transducers, for example, in a joystick, are controlled by potentiometers.

Principle of Potentiometers

A potentiometer works on the principle that the voltage drop along the wire is directly proportional to the length of the wire. The potentiometer works without drawing any current from the voltage source.

Working of Potentiometer 

The Potentiometer is made up of a resistive element, a sliding contact (wiper) that moves along the element, making good electrical contact with one part of it, has electrical terminals at each end of the element along with a mechanism that moves the wiper from one end to the other and a housing containing the element and wiper. The potentiometer uses the comparative method, which is more accurate than the deflection method. Therefore, it is mainly used in places where higher accuracy is required.

To understand its working, consider the following case:

Two batteries are connected through a galvanometer and have the same EMF ‘E’. The negative terminals of both batteries are connected, while the positive terminals of the batteries are connected through a galvanometer. Since the EMF aboard the batteries is the same, the galvanometer will show a null deflection, indicating no current flowing through the circuit. This is a precise example of how the potentiometer works.

Comparison of EMF of Two cells

The apparatus required to compare the EMF of two given primary cells with the help of a potentiometer is –

• Potentiometer

• Daniel Cell

• Leclanche Cell

• Low resistance Rheostat

• Ammeter

• Voltmeter

• Galvanometer

• A one-way key

• A two-way key

• Set Square

• Jockey

• Resistance Box

• Connecting wires

• Piece of sandpaper

The procedure to compare the EMF of two given primary cells with the help of a potentiometer is –

1. Gather all the instruments mentioned and prepare connections.

2. Remove the insulation from the ends of connecting copper wire with the help of sandpaper.

3. The EMF of the battery (E) and the EMF’s of the cell (E1 and E2 ) should be measured to see if E1 >  E2 and E2 > E1.

4. The battery’s positive pole should be connected to the zero ends (P) of the potential meter and the negative pole should be connected through the one-way key, low resistance rheostat, and the amateur to the other end of the potentiometer (Q).

5. The positive poles of the cells should be connected to the terminals at the zero ends (P) and the negative poles should be connected to terminals a and b of the two–way key.

6. The common terminal c of the two-way key should be connected through a galvanometer (G) and the resistance box to the jockey J.

7. By making the rheostat resistance zero, take maximum current from the battery.

8. Take out the 2000 ohm plug from the resistance box.

9. The direction of the deflection in the galvanometer should be noted down by pressing the jockey at the zero ends. Similarly, press the jockey at the other end of the potentiometer wire. The connections are correct if the deflection is in the opposite direction to that in the first case.

10. Move the jockey smoothly over the potentiometer up to a point where the galvanometer shows no deflection. Now, put the 2000 ohm plug back into the resistance box and accurately obtain the null point position.

11. Note down the length l1 of the wire for the cell, E1.

12. The current as indicated by the ammeter should also be noted down.

13. Cell E1 should be disconnected from the plug and cell E2 should be connected by inserting the plug into the gap of the two–way key.

14. Take out the 2000 ohms plug from the resistance box and slide the jockey along the potentiometer wire to obtain the point where there is no deflection. By putting the 2000 ohm’s plug back in the resistance box, obtain the null point for E2 and note down the length l2 of the wire in this position for the cell E2. 

15. Repeat this process by increasing the current and adjusting the rheostat to get three sets of observation.

From the different sets of values, we get the formula for the potentiometer.

E1/E2 = l1/l2

Measurement of Internal Resistance of the Cell by potentiometer

The apparatus required  potentiometer to measure internal resistance of a cell  is:

• Galvanometer 

• A battery

• Potentiometer

• Rheostat of low resistance

• A fractional resistance box

• Ammeter

• Numbers keys (one-way)

• Connecting wires

• A jockey

• High resistance box

• Sandpaper

• Leclanche cell

• Voltmeter

A potentiometer is used to measure the internal Resistance Office cell and compare the EMF of two cells and potential differences across the resistor. 

To measure the Internal resistance of the cell relationship between internal resistance and EMF of a cell is given by:

e = I (r + R)

Or  e = V + Ir

V is the potential difference (also known as the voltage) across the cell, which is the amount of energy the cell can provide when the current (I) is flowing through the circuit.

The procedure to measure the internal resistance of the cell with the help of a potentiometer is,

1. Gather all the instruments mentioned and prepare connections.

2. Remove the insulation from the ends of connecting copper wire with the help of sandpaper.

3. The plugs in the resistance box should be tight.

4. The e.m.f of the cell and battery is more than that of the cell.

5. Rheostat resistance can be made minimum by taking maximum current from the battery.

6. To check if the circuit connections are correct, the galvanometer deflections should be in the opposite direction. This is done by inserting the key K1 and making a note of the ammeter reading.

7. To obtain the null point on the fourth wire, the rheostat should be adjusted without inserting the key K2.

8. Record your observations.

Potentiometer Sensitivity

Potentiometer sensitivity means the smallest potential difference that can be measured using the potentiometer. This can be achieved by decreasing the potential gradient by increasing the length of the wire or reducing the current in the potential meter using a rheostat. The sensitivity of the potentiometer is inversely proportional to the potential gradient.

Conclusion

In this article, we learned about the Potentiometer and the comparison of the EMF of two cells by using a potentiometer. We also learned about the measurement of Internal Resistance of the Cell by using a potentiometer and Potentiometer Sensitivity. To better understand this chapter, other topics such as moving-coil galvanometer and Kirchhoff’s Law are suggested to the user.