For the circuit would the balancing length increase, decrease or remain the same if (i) `R_(1)` is decreased (ii) `R_(2)` is increased, without any change (in each case) in the rest of the circuit ? Justify your answer in each case.

Explanation

(i) When `R_(1)` is decreased, the balancing length decreases. It is because as `R_(1)` decreases, the current in the potentiometer circuit increases. Due to it, the potential gradient of potentiometer wire increases. As a result of it the same emf will be balanced on smaller length of potentiometer wire.
(ii) When `R_(2)` is increased, the balancing length increases. It is because as `R_(2)` increases, the current `I( = epsilon/r+R_(2))` decreases. This increases the terminal pot. diff. `V (epsilon - Ir)` across the unknown cell. As a result of it, the terminal potential difference of cell `epsilon` will be balanced on larger length of potentiometer wire.