With two resistance `R_1 and R_2 (>R_1)` in the two gaps of a metre bridge the balance was found to be 1/3 m from the zero end. When a `6 Omega `resistance is connected in series with the smaller of the two resistance, the point is shifted to 2/3 m from the same end, then `R_1 and R_2` are

Options

A. 4, 2
B. 2, 4
C. both (a) and (b)
D. neither (a) nor (b)

Answer

B

Explanation

`(P)/(1//3)=(Q)/(1-(1//3)),l=1m`
or `3P=(3)/(2)QorP=(Q)/(2)" "...(i)`
When `6Omega` resistance is connected in series with P, then the balance point shifted as
`(P+6)/(2//3)=(Q)/(1//3)or(3(P+6))/(2)=3Q`
or `P+6=2Q" "…(ii)`
From (i), `(Q)/(2)+6=2Qor,6=2Q-(Q)/(2)=(3Q)/(2)`
or, `Q=4`. Then `P=2`