State working principle of potentiometer. Explain how the balance point shifts when value of resistor R increases in the circuit of potentiometer, given below.

Explanation

A potentiometer works on the principle that for a constant current flowing through the potenti-ometer wire of uniform cross-section the fall in potential is directly proportional to the length. When value of resistor R is increased in the circuit of potentiometer, current flowing through potentiometer wire due to driver cell V decreases and consequently the value of potential gradient .k. along potentiometer decreases.
Mathematically `I=(epsilon)/(R+R_(1))`, where `epsilon=emf` of driver cell and `R_(1)=` resistance of potentiometer wire and
`k=1(R_(1))/(L)`, where L = total length of potentiometer wire AB.
`rArr" "k=(epsilon R_(1))/((R+R_(1))L)`
Due to decrease in the value of .k., the balance point will shift towards right i.e., the balancing length increases.