To compare the E.M.F. of two cells with a Potentiometer. Theory

Experiment Name: To compare the E.M.F. of two cells with a Potentiometer.

Theory: If a current i amperes flows through the potentiometer wire of length L cm and resistance R_p ohms and if R is the external resistance which is in series with the potentiometer circuit (in figure-1), then

і =

Where E is the e.m.f of the cell C.

Then the potential drop V across the end of the potentiometer wire is

V = і ×R_p = 

Hence the potential drop per centimeter of the wire,

ρ =   =  ×   =  ´   volts.

If the potentiometer has 10 wires of 1 meter each.

 If the cells  C₁  and  C₂  require lengths  l₁  and  l₂  respectively of the potentiometer wire for balance, then the e.m.f. E₁ and  E₂  of the cells C₁ and  C₂ are given by

E₁ = ρl₁ =  ´   ´ l₁ volts …………………… (1)

And E2 = ρl₂ =  ´   ´ l₂ volts …………………… (2)

Then the ratio of the e.m.fs. Of the two cells

 =   ´  =  …………………….. (3)

Or,  =   …………………….. (4)

By simply determining the balancing lengths l₁ and l₂, the e.m.f. of the two cells can be compared by using equation (3) when both are unknown. If the e.m.f. of any one of them is known then the e.m.f. of the other can be determined by using equation (4). Alternately, the e.m.f. of each cell can be calculated by using equations (1) and (2) from known values of E, R and R_p.

Apparatus:  Potentiometer AB, Storage battery E, Two cells C1 and C2 (may be Leclanche and a Daniel cell) whose e.m.f. Are to be compared, a rheostat R_h, (app. 2500 ohms), a high resistance R’, a zero-centre galvanometer, a two-way key, plug keys, connecting wires, etc.

Experimental Procedure:

Arrange the required materials on a table and make the connections as per the connection diagram.

1. Tight the plugs of the resistance box. Note the reading on the ammeter.

2. To test the connection, insert plug in the one way key k and also in between the terminals of the two ways key. Introduce a sufficiently high resistance on the resistance box (R.B). Place the jockey at the two end points of the wire. Press the jockey at both end of the potentiometer wire and note the deflection in galvanometer. If the galvanometer shows opposite deflection, the connections are correct.

3. Now, gently slide the jockey along the potentiometer wire and stop when null point is obtained.

4. Measure the length l₁ between this point and the end P of the potentiometer. It is the balancing length for the cell E₁.

5.Disconnect the cell E₁ by removing the plug from the gap ac of the two way key and connect the cell E₂ by inserting plug into the gap bc of the two way key.

6. Again slide the jockey along the potentiometer wire to obtain the null point. Measure the new balancing length l₂ for the cell E₂ based on this point.

7. Make sure that the reading on the ammeter is constant throughout the observation.

8. Repeat the experiment by increasing the current by adjusting the rheostat and record the observations.

9. Each time, the ratio between the emf’s of the given cells can be calculated using the relation,

Experimental Data:

Table for the measurement of:

No. of obs.	Cell	Null points			Total length cm	=	Mean
		On wire number	Scale reading cm	Mean scale reading cm
01
02
03
04

Calculations:

(і) .   =
(іі).   =
(ііі).   =

(іv).   =

Mean,    =

Results:  The e.m.f. of two cells is……………………….

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