# To Determine The Internal Resistance of A Given Primary Cell Using Potentiometer

## Aim/Aim of Experiment

To determine the Internal Resistance of a given Primary Cell using Potentiometer.

## Apparatus/Material Required

• A Potentiometer
• A Battery (Battery Eliminator)
• 2 One-way Keys
• A Rheostat (low resistance)
• A High Resistance box
• A Frictional Resistance box
• A Galvanometer
• An Ammeter
• A Voltmeter
• A Cell (Leclanche cell)
• A Jockey
• A Set Square
• Connecting wires
• A piece of Sand paper.

## Theory

Potentiometer an instrument used to measure Potential difference (V) and e.m.f. of a cell or also used to compare the e.m.f. of two cells and the potential difference across a Resistor.

When a resistance R is connected across a cell of emf E and internal resistance r, then the current I in the circuit is given by

I = E/(R+r) or E = I(R+r) (Eq. 1)

The potential difference V (= RI ) across the two terminals of the cell then,

V = E/(R+r)R (Eq. 2)

Thus, E/V = 1+(r/R) or r = [(E/V)-1]R (Eq. 3)

So the relation between Potential difference, emf, and Internal resistance of a cell is given by E = I(R+r) or r = [(E/V)-1]R

If l1 and l2 are the distances of the balance null point (balancing Lengths) from end A of the potentiometer for an open and a closed circuit (without shunt or with the shunt), then E is proportional to l1 and V is proportional to l2.

E/V=l1/l2 (Eq. 4)

Now from (Eq. 3) & (Eq. 4)

r = [(l1-l2)/l2]R (Eq. 5)

where R is the shunt resistance in parallel with the given cell, l1 and l2 are the balancing lengths without shunt and with the shunt and r is the Internal resistance of the cell.

## Procedure

1. Connect different electrical components as shown in the circuit diagram.
2. Clean the ends of the connecting wires with sand paper and make tight connections according to the circuit diagram.
3. The plugs in the resistance box should be tight.
4. Check the e.m.f. of the battery and cell and see that e.m.f. of the battery is more than that of the given cell, otherwise null or balance point will not be obtained (E’>E).
5. Using the Rheostat resistance take maximum current from the battery, making rheostat resistance small.
6. To check the correctness of the connections take out 2000 Ω resistance plug from the resistance box, Place the jockey first at the end P of the wire and then at the end Q, If the galvanometer shows deflection in opposite directions in the two cases means connections are correct. Also check the ammeter reading by inserting the plug in the Key (K1).
7. Adjust the rheostat without inserting the plug in the Key (K2), so that a null point is obtained on the fourth wire of Potentiometer.
8. Take out the 2000 ohms plug again from the resistance box R.B. Introduce the plugs in key K1, as well as in key K2.
9. Take out a small resistance (1-5 Ω) from the resistance box R connected in parallel with the cell.
10. Slide the jockey along the potentiometer wire and obtain null point.
11. Now insert 2000 ohms plug back in its position in R.B. and if necessary make further adjustment for sharp null point.
12. Measure the balancing length l1 from end P.
13. Remove the plug keys at K1 and K2, wait for some time and repeat the activity for the same value of current (as shown by the ammeter).
14. For different values of R, repeating the each observation twice.
15. Record your observations as given below.

## Observations

• Range of Voltmeter = 30V.
• Least count of Voltmeter = 1V.
• E.M.F. of Battery = 8V.
• E.M.F. of Cell = 1.4V.

## Calculations

1. For each set of observation find mean and l2 and write in column 3c and 3f.
2. Calculate value of r for each set and write it in column 5.
3. Take mean of values of r recorded in column 5.

## Result

The internal resistance of the given cell is = 28.83 ohm.

## Precutions

1. The primary cell whose internal resistance is to be determined should not be disturbed during the experiment or else its internal resistance may change.
2. The e.m.f. of the battery should be greater than that e.m.f. of the primary cell.
3. For one set of observation the ammeter reading should remain constant.
4. Current should be passed for short time only, while finding the null point.
5. The rheostat should be placed so that initial null point lies on last wire of the potentiometer.
6. Ensure that the cell should not be disturbed during the experiment.
7. The Jockey should not be rubbed against the Potentiometer wire.

## Sources of Error

1. Potentiometer wire may not be of uniform cross – section.
2. The e.m.f. of the battery is less than that e.m.f. of the primary cell (E'<E).
3. E.M.F. of the auxiliary battery producing the drop of potential along the wire may not be constant throughout the course of the experiment.
4. Heating of the potentiometer wire by current may introduce some error.
5. Cell is distributed during the experiment.

## Viva Voice Questions with Answers

1. What is a potentiometer?

Answer: It is an instrument used to measure potential difference or e.m.f. of a cell.

2. What is the merit of a potentiometer over a voltmeter in measurement of e.m.f. of a cell?

Answer: E.M.F. measured by potentiometer is more accurate because the cell is in open circuit, giving no current.

3. What do you mean by internal resistance of a cell?

Answer: It is the resistance offered by the electrolyte to the flow of ions to their respective electrodes.

4. On what factors does the internal resistance of a cell depend?

Answer: Internal resistance of a cell depends upon following:

• Distance between electrodes and is directly proportional to its Facing surface area of the electrodes in electrolyte and is inversely proportional to it.
• Nature of electrolyte and is inversely proportional to its specific conductivity.
• Temperature increases, the internal resistance decreases and vice-versa.
• Internal resistance increases with the use of cell.

5. Does the internal resistance depend on the current drawn from the cell?

Answer: Yes, the internal resistance usually increases as more current is drawn from the cell.

6. Can we find the internal resistance of an accumulator or secondary cell?

Answer: No, the internal resistance of an accumulator is so small (= 0.01Q) that this method cannot be used.

7. What other measurements can be made by a potentiometer?

Answer: A potentiometer can be used for measuring small thermo e.m.f. It can also be used for calibrating voltmeter and ammeter. It can be used to measure and control stress, temperature, radiation, pH, frequency etc.

8. Can you measure e.m.f. by a voltmeter?

Answer: No. The voltmeter measure the terminal potential difference of a cell because it draw some current V = E-Ir, when I≠0, then V < E.

9. Which voltmeters can be used to measure the e.m.f. of the cells?

Answer: Electric voltmeter. Vacuum tube volt meter (VTVM) after nearly infinite resistance. So the current drawn is minimum, nearly zero. These two voltmeter are act as ideal voltmeter.

10. Does the at position of balance point (null point) mean no current through the potentiometer?

Answer: No. the current always flow in potentiometer wire. These is no current in galvanometer because there is no current drawn from the cell whose e.m.f. is to be measured or compared.

11. Does the potentiometer is used to determine the internal resistance of (i) primary cell (ii) secondary cell?

Answer: The potentiometer is used to determine the internal resistance of primary cell only but not secondary cell because of very small resistance (0.02Q).

12. What are the factors on which the e.m.f. of a cell depends?

1. Nature of electrodes,
2. Nature of electrolyte,
3. Concentration of electrolyte,
4. Temperature of electrolyte.

13. Why is a potentiometer preferred over a voltmeter for measuring the e.m.f. of cell?

Answer: A potentiometer draws no current from the cell whose e.m.f. is to be measured. On the other hand, the voltmeter always some current. Thus e.m.f. measured by voltmeter will be slightly less than the e.m.f. measured by potentiometer (V = E-Ir).

14. Why do we prefer a potentiometer with a longer bridge wire?

Answer: When the bridge wire is longer, the potential gradient is smaller. Smaller the potential gradient, more is the sensitivity of potentiometer wire.

15. What are the factors on which internal resistance of a cell depends?

1. Nature of electrodes,
2. Nature of electrolyte,
3. Concentration of electrolyte,
4. Temperature of electrolyte,
5. Distance between the electrodes,
6. The area of electrodes immersed in electrolyte.

16. Can we consider the potentiometer as an ideal voltmeter?

Answer: Yes, At null point, the potentiometer does not draw any current. Hence it measure the emf. The potentiometer is equivalent to an ideal voltmeter.

V = E-Ir,

let I=0, Then V=E.

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