## Factors affecting internal resistance of a cell

Introduction: There is a great need of batteries in our daily use electronic appliances and the use is increasing every day. Thus , the batteries need to be made more powerful  so that their potential can be increased greatly. Thus , this project report is based on practical analysis for the factors affecting the internal resistance of a cell. When the internal resistance of the cell is decreased we can increase the potential difference across it , and hence make it more reliable.

# Objective

To study the various factors on which the internal resistance of a cell depends.

Apparatus A Potentiometer , a battery (battery eliminator) , two way keys , a rheostat of low resistance , a galvanometer , a high resistance , an ammeter , a cell ,  a Jockey , a set square , connecting wires , water bath , thermometer(0-100°C) , burner , tripod stand , wire gauge .

Theory The internal resistance of a cell is the resistance offered by its electrolyte to the flow of ions . The internal resistance of a cell

• is directly proportional to the distance between the electrodes.
• is inversely proportional to facing surface area of the electrodes in electrolyte.
• decreases with increase in temperature of electrolyte.
• is inversely proportional to concentration of electrolyte.

The internal resistance of a cell is given by

r = (( l1-l2)/l1)R

where l1  , l2  are the balancing lengths without resistance and with resistance (shunt) , respectively and R is the shunt resistance in parallel with the given cell.

#### Procedure

Step 1

1. Draw the circuit diagram showing the scheme of connections.
2. Clean the ends of the connecting wires with sand paper and make tight connections according to the circuit diagrams.
3. Tight the plugs of the resistance box.
4. Check the e.m.f. of the battery and cell and see that e.m.f. and see that e.m.f. of the battery is more than that of given cell ,otherwise null or balance point will not be obtained (E’ >E).
5. Take maximum current from the battery , making rheostat resistance small.
6. To test the corrections of the connections.(insert the plug in the key and note the ammeter reading .Take out 2000 ohm resistance plug from resistance box. Place the jokey first at the end P of the wire and then at the end Q. If the galvanometer shows deflection in opposite direction in the two cases the connections are correct).
7. Without inserting the plug in the key adjust the rheostat so that a null point is obtained on the 4th wire of potentiometer.
8. Insert the 2000 ohm plug back in the position in resistance box and by slightly adjusting the jockey near the previous obtained position of null point, obtain null point position accurately, using a set square.
9. Measure the balancing length between the point and the end P of the wire.
10. Take out the 2000 ohm plug again from the resistance box B. introduce plugs in the key ,as well as in key . Take out small resistance (1-5 Ω) from the resistance box R connected in parallel with the cell.
11. Slide the jockey along the potentiometer wire and obtain null point.
12. Insert 2000 ohms plug back in its position in B. and if necessary make further adjustment for sharp null point.
13. Measure the balancing length from end P.
14. Remove the plug keys at and .Wait for some time and for the same value of current (as shown by ammeter) repeat the steps 7 to 13.
15. Repeat the observations for diffrent values of R repeating each observation twice.
16. Calculate the internal resistance of cell by using the above relation for r.

Step 2 To see the effect of distance between the electrodes on internal resistances keeping the other factors constant ,vary separation between electrodes and measure internal resistance in each case.
Step 3 To see the effect of the temperature of electrolyte on internal resistance by keeping other factors constant. Keep primary cells in water bath to heat the electrolyte. Determine the internal resistance at various temperatures.
Step 4 To see the effect of concentration (nature) of electrolyte on internal resistance by : Keeping the other factors constant , decrease concentration of electrolyte  by adding the distilled water and determine internal resistance of cell in each case .

Observations

 S.No. Ammeter Reading Pos. of null point ( cm ) Shunt Resistance r = (( l1-l2)/l1)R ( A ) With R (l1 ) Without R ( l2 ) R ( Ω ) Ω 1. 0.3 660.5 35.5 1 0.94 2. 0.3 660.5 77.2 2 1.77 3. 0.3 660.5 108.3 3 2.51

Table for effect of separation between electrodes

 S.No. Separation between Balancing length Balancing length r = (( l1-l2)/l1)R r/d Electrodes-d (cm) (cm) ( l1 ) (cm) (l2) ( Ω ) 1. 1.2 326.6 276.9 0.456 0.38 2. 2.5 320.7 219.1 0.95 0.38 3. 3.7 660.5 350.9 1.406 0.38

Table for effect of temperature

 S.No. Temper-ature l1 l2 Resistance r = (( l1-l2)/l1)R Tr (T) °C (cm) (cm) R (Ω) (Ω) (ΩK) 1. 40 325 12 1 0.96 301.44 2. 32 552 23.6 1 0.95 291.96 3. 27 660.5 35.5 1 0.94 283.87

Conclusions

1. The Electromotive Force of the cell is constant and is equal to E = 0.98  Volt
2. The internal resistance of a cell is directly proportional to the separation between the electrodes.
3. The internal resistance of a cell is inversely proportional to the area of the electrodes dipped in electrolyte.
4. The internal resistance of a cell is inversely proportional to the temperature of electrolytes.
5. The internal resistance of a cell is inversely proportional to the concentration of the electrolyte.

Precautions

1. The connections should be neat , clean and tight.
2. The plugs should be introduced in the keys only when the observations are to be taken.
3. The positive polls of the battery E and cells E1 and E2 should , all be connected to the terminal at the zero of the wires.
4. The jockey key should not be rubbed along the wire. It should touch the wire gently.
5. The ammeter reading should remain constant for a particular set of observation. If necessary , adjust the rheostat for this purpose.
6. The e.m.f. of the battery should be greater than the e.m.f.’s of the either of the two cells.
7. Some high resistance plug should always be taken out from resistance box before the jockey is moved along the wire.
8. The e.m.f. of the battery should be greater than that of the cell.
9. For one set of observation the ammeter reading should remain constant.
10. Current should be passed for short time only , while finding the null point.
11. Rheostat should be adjusted so that initial null point lies on last wire of the potentiometer.
12. Cell should not be disturbed during experiment.
13. Jockey should not be rubbed against the potentiometer wire.

sources of error

1. The auxiliary battery may not be fully charged.
2. The potentiometer wire may not be of uniform cross-section and material density throughout its length.
3. End resistances may not be zero