Potentiometer has multiple uses. It is based on the principle that when constant current flows through a wire of uniform area of cross-section then potential drop along its length is directly proportional to corresponding length.
i.e. \( V \propto l \) ; \( V = K l \)
Various uses of potentiometer on :
- To measure potential differences between any two points in an electrical network
- To compare emf of a cell
- To measure emf of a cell
- To measure internal resistance of a cell etc:
Answer the following question related to potentiometer.
In the given potentiometer on increasing value of R:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Balancing length will increases
The balancing length is \( l = E/k \), where \( k \) is the potential gradient of the wire AB. The resistance R is in series with the driver cell V and the wire, so it controls the current in the wire.
If \( R_{AB} \) and \( L \) are the resistance and length of the wire,
\( \displaystyle I = \frac{V}{R + R_{AB}} \)
\( \displaystyle k = \frac{I\,R_{AB}}{L} = \frac{V\,R_{AB}}{(R + R_{AB})\,L} \)
When R is increased, the current \( I \) falls, so the potential gradient decreases. A longer piece of wire is then needed to balance the same emf E:
\( \displaystyle l = \frac{E}{k} \;\Rightarrow\; l \text{ increases} \)
Hence the balancing length increases.