Question

the+'balancing+lengths',+on+the+potentiometer+wire+are+found+to+be+3+m+and+2.85+m,+respectively.+The+value+of+internal+resistance+of+the+cell+is+[AIPMT+2014]

Answer 1

Given, e = 2V and l= 4m Potential drop per unit length \phi =\frac{e}{l}=\frac{2}{4}=0.5V/m For the first case, Þ e'=\phi {{l}_{1}}\,\,\,\,\,\,\,\,\,....(i) (e'® emf of the given cell) For the second case, V=\phi {{l}_{2}}\,\,\,\,\,\,\,\,\,....(ii) From Eqs. (i) and (ii), e'/V={{l}_{1}}/{{l}_{2}} e'=l(r+R) and V=lR for the second case So,  r=R\left( \frac{{{l}_{1}}}{{{l}_{2}}}-1 \right)=9.5\left( \frac{3}{2.85}-1 \right)=9.5(1.05-1) =9.5\times 0.05=0.475\simeq 0.5\Omega