INVESTIGATORY PROJECTAim:To study various factors on which the internal resistance/EMF of a cell depends.

Concepts:Internal Resistance of a cell

1. When a cell connected in a circuit is made to send current through the circuit by closing the key, current flows from the positive pole to the negative pole of the cell in the external part of circuit and flows from the negative pole to the positive pole through the electrolyte inside the cell. During the passage of the current through the interior of the cell, electrolyte offers some resistance to the flow of current. The resistance offered by the electrodes and the electrolyte to the passage of current through the interior of the cell is called the internal resistance of the cell. It is donated by the symbol ‘r’.

2. E.M.F. of a cell (E). The maximum potential difference that exists between the terminals of a cell, when cell is in open circuit i.e. when it is not sending any current through the circuit is called e.m.f. of the cell. It is donated by the symbol ‘E’.Terminal potential difference (V). The potential difference that exists across the terminal of a cell when the cell is sending current in the circuit, is called the terminal potential difference of the cell. It is donated by the symbol ‘V’.

3. Relation Between E and V. When a cell of terminal resistance ‘r’ is sending current I through a circuit, then

E=V+I.r

4. Factors on which the Internal Resistance of a cell depends. Internal resistance of a cell depends upon the following factors:

i. distance between electrodes ii. common area of electrodes inside the electrolyte

iii. nature of the electrolyte iv. amount of current drawn from the cell.

Nature of Dependence on:i. Distance between Electrodes. Internal resistance of

a cell is directly proportional to the distance between the electrodes i.e. the length of the electrolyte through the current passes through the cell.

ii. Common Area of Electrodes. It is inversely proportional to the common area of electrodes (or plates) dipping in the electrolyte.

iii. Nature of Electrolyte. Internal resistance of a cell is inversely proportional to the specific conductivity of the electrolyte. Specific conductivity is reciprocal of specific resistivity or specific resistance of the electrolyte.

iv. Amount of Current Drawn from a Cell. Internal resistance of a cell also depends upon the amount of current drawn from the cell. Beyond a certain critical value of current drawn from a cell, its internal resistance increases with the increase in the value of current drawn from it. There is, however, no definite mathematical relation between the two.

Apparatus

An improvised simple voltaic cell, a multimeter, a resistance box (0 - 50ῼ range), a plug key, beakers of 500 mL and 200 mL capacity, high resistance voltmeter.

Description of the improvised Primary Cell 1. Take a beaker of capacity 500 mL and paste on it a

vertical strip of a cm graph paper such that the lower edge of strip touches the bottom and upper edge touches the top of the beaker. Mark on the graph strip, the distances in centimeter from bottom to the top (Fig. D-1.1).

2. Electrodes: Take two plates of size 5 cm X 12 cm X 1 mm each cut out of sheets of copper and zinc. One threaded bolt of length 8 cm and diameter about 3 mm is soldered in the middle of each of the plates. Each of the bolts is provided with a pair of tightly fitting nuts and a connecting terminal at the top.

3. A thin lid of wooden sheet (ply) with a rectangular slot of width slightly more than the diameter of bolts (i.e., about 3.5mm) and length about 12 cm, is taken and metallic plates with their parallel faces facing each other, are fitted into the slot of the lid and tightened by the nuts. 1 molar solution of H₂SO₄ is filled in the beaker up to (3/4) th of its height and the metallic plates (called electrodes) are dipped in the solution without touching the bottom of the beaker. This arrangement (shown in Fig. D-1.1) is your improvised cell needed for the activity.

Theory:The difference between the e.m.f. (E) of a cell and its terminal p.d. (V) is governed by the relation,

E-V=I . r

where r is the internal resistance of the cell. The increase in the difference (E-V) for the same current shows an increase in internal resistance and vice versa.

Procedure:A. Effect of change of distance

between the plates:1. Keep a distance of about 10 cm in between the plates, dip then

completely in the solution and fix them in position with the help of nuts N₁ and N₂.

2. Take out a suitable resistance of 4 ohms from the resistance box (R.B.). Plug in the key K and measure the terminal potential difference (V) with the help of a high resistance voltmeter of a multimeter.3

3. Open the circuit by taking out the plug from the key K and again measure the drop of potential across the terminals of the cell in the open circuit. This p.d. gives the e.m.f. (E) of the cell.

4. Now change the distance between the plates to 5 cm and repeat the steps 2 and 3 taking out a suitable resistance from R.B. such that the current is same as in step 2.

5. Take three more sets of observations, keeping the separation between plates as 6 cm, 4 cm and 2 cm.

6. Record your observations as detailed below :

ObservationsWith change of Distance

between ElectrodesTable 1.1

No. of Obs. Distance between

electrodes (cm)

V(volt)

E(volts)

Difference (E-V)

(volt)

Inference

1. 10.02. 8.03. 6.04. 4.05. 2.0

B. Dependence on Common Area of Electrodes

Procedural Steps7. Keep a fixed distance between the electrodes (or plates) say 5 cm and keep top edges of the plates just immersed in the electrolyte.

8. Take out a suitable resistance from the resistance box and measure the terminal p.d. (V) by the voltmeter.

9. Open the circuit by taking out the plug from key K and measure e.m.f. of the cell (E) by multimeter or voltmeter.

10. Pull both the plates out of the electrolyte by 2 cm so that the common dipped area in the solution decreases. Now repeat the steps 8 and 9.

11. Take two more sets of observations by further pulling electrodes out of the electrolyte suitably and repeat steps 8 and 9 again.

12. Record your observations as given below:

For dependence on common area of plates inside the electrolyte.

Table -1.2No. of Obs. Length of

electrodes inside

electrolyte* (cm)

V(volt)

E(volt)

Difference (E-V) (volt)

Inference

1.

2.

3.

4.

*A decrease in length of electrode dipped in electrolyte will decrease the effective area of electrodes inside the electrolyte.

C. Dependence on the Concentration of Electrolyte13. Lower down the plates suitably in the solution and set the gap between the plates about 5 cm. Let the concentration of the electrolyte solution be 1 molar (IM) ** to start with. If it is not so, check up the concentration of the acid solution and prepare it accordingly.

14. Take out suitable resistance from the resistant box and measure the terminal potential difference ‘V’ and e.m.f. ‘E’ of the cell as explained earlier.15. Pour out solution of the cell in a bigger graduated cylinder and add calculated quantity of distilled water to increase the volume of the solution so that the concentration reduces to 0.8 M.16. Repeat step (14) for measuring V and E of the cell. 17. Take two more sets of observations with concentration of 0.6 M and 0.4 M, of the electrolyte.18. Record your observations as detailed below:

Observations:With change of concentration of electrolyte

Table D-1.3No. of Obs. Concentration

(molar)V

(volt)E

(volt)Inference

1.2.3.4.

Conclusion 1. Internal resistance of a primary cell increases with the increase in distance

between electrodes.2. Internal resistance increases with decrease in common area of electrodes

dipped in the electrolyte.3. Internal resistance increases with decrease in concentration of the

electrolyte.

Precautions

1. All connections in the circuit should be neat and tight. All plugs in resistance box should also be tight.

2. Positive terminal of the voltmeter should be connected to the positive terminal of the cell.

3. To decrease the common area of the electrodes dipped in the electrolyte, the plates.