The circuit diagram given in the figure shown the experimental setup for the measurement of unknown resistance by using a metre bridge. The wire connected between the points P and Q(PQ = 100 cm) has uniform cross-sectional area and its resistivity is directly proportional to the distance from point P. Null point is obtained with the jockey J with `R_1 and R_2` in the gaps. If `R_1 and R_2` are interchanged, the jockey has to be displaced through a distance from the previous position along the wire to establish the null point. If the ratio of `R_1/R_2=3` , the value of `Delta` (in cm) is: [Ignore any end corrections]

Options

A. 50
B. `50(2sqrt3)`
C. `50(sqrt5-2)`
D. `50(sqrt3-1)`

Explanation

From the given circuit diagram `R_1/R_2=x^2/((100)^2-x^2)` `implies x=50sqrt3`
Also, `R_2/R_1=y^2/((100)^2-y^2) implies y=50, Delta 50(sqrt3-1) cm`