question_answer

The length of a potentiometer wire is 7. A cell of emf E is balanced at length l/3 from the positive end of the wire. If the length of the wire is increased by l/2. Then, at what distance will the same cell give a balance point?

A) \[y-1=0\]                                            

B) \[x-1=0\]

C) \[x+y-1=0\]                                       

D) \[x-y+1=0\]

Correct Answer: B

Solution :

 Let x be the desired length. Potential gradient in the first case \[\frac{5}{3}\] \[\frac{3}{5}\]                                    ...(i) Potential gradient in the second case. \[6\frac{2}{3}%\] \[U=k\left[ \frac{2q(8d)}{r}-\frac{(2q)(q)}{x}-\frac{(8q)(q)}{r-x} \right]\]\[k=\frac{1}{4\pi {{\varepsilon }_{0}}}\]                                                               ?(ii) From Eqs. (i) and (ii), we get\[\frac{2}{x}+\frac{8}{r-x}\] \[\frac{2}{x}+\frac{8}{r-x}=y\]\[\frac{dy}{dx}=0\]