Question

Define the term potential gradient. Using this concept, explain the method for comparison of emfs of two primary cells using a potentiometer. Establish the relation used. Write two possible causes of potentiometer giving only one-sided deflection.

Accepted Answer

The potential drop per unit length of the potentiometer wire is known ns potential gradient. It is given by

. $K = \frac{V}{I}$

The practical unit of potential gradient $= V m^{- 1}$

Comparison of emf of two primary cells. The Figure given below shows the circuit diagram for comparing the emf of two cells. A constant current is maintained in the potentiometer wire $A B$ by means of a battery of emf $ε$ through a key $K$ and rheostat $R_{h}$ Let $ε_{2}$ and $A$ be the emf of the two primary cells which are to be compared. The positive terminals of these cells are connected to the end $A$ of the potentiometer wire, and their negative terminals are connected to a high resistance box a galvanometer $G$ and a jockey $J$ through a two-way key. A high resistance $R$ is inserted in the circuit from resistance box R.B. to prevent excessive currents flowing through the galvanometer.

Jokey is moved to $N_{1}$ which is at a distance li from A to find the balancing length

Applying loop rule to $A N_{1} G 3 I A$ .

$ϕ I_{2} + 0 - E_{1} = 0$

Similarly for $E_{2}$ balanced against $I_{2} {(A N)}_{2}$

$ϕ I_{2} + 0 - E_{2} = 0$

$\frac{E_{1}}{E_{2}} = \frac{I_{1}}{I_{2}} . . . . . . (1)$

thus we can compare the emf's of any two sources.Generally one of the cells is chosen as a standard cell whose emf is known to a high degree of accuracy. The emf of the other cell is then calculated from Equation (1)

Two possible causes for one sided deflection in a potentiometer experiment.are-

(i) The emf of the cell connected in main circuit may not be more than the emf of the primary cells whose emfs are to be compared .
(ii)The positive ends of all cells are not connected to the same end of the wire .

S L Arora Solutions for Chapter: Current Electricity, Exercise 6: Text Based Exercises

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