Question

The potentiometer wire AB shown in the figure is 50 cm long. When AD = 30 cm, no deflection occurs in the galvanometer. Find R.

Answer 1

It is given that at point D, there is no deflection in the galvanometer, i.e. the bridge is balanced

\[\Rightarrow \frac{R_{AD}}{R_{DB}} = \frac{6}{R}\]

According to the principle of a potentiometer,

\[\frac{R_{AD}}{R_{DB}} = \frac{l_{AD}}{l_{DB}}\]

\[ \Rightarrow \frac{6}{R} = \frac{30}{20}\]

\[ \Rightarrow R = \frac{20 \times 6}{30} = 4  \Omega\]