In the figure shown below, the maximum and the minimum possible unknown resistance (X), that can be measured by the post office box are `X_(max)` and `X_(min)` respectively. Then the ratio of these two resistances is : (In this experiment we take out only one plug in arm AB and only one plug in arm BC, but in arm AD we can take out any no. of plugs) :

Options

A. `3 xx 10^5`
B. `5 xx 10^5`
C. `7 xx 10^5`
D. `9 xx 10^5`

Answer

D

Explanation

`(P)/(Q)=(R)/(X)`
`X = (Q)/(P)R`
`(X)_(max) = (Q_(max))/(P_(min)) xx R_(max) = (1000)/(10) xx 9000 = 900 k Omega`
`(X)_(min) = (Q_(min))/(P_(max))xxR_(min) = (10)/(1000) xx 100 = 1 Omega`
(D) as `X = (Q)/(P) R` so to increase accuracy
`(P)/(Q)` ratio should be increased, so that R can be divided by a larger number. (Read the experiment from "Measurement errors and experiment sheet")