Question

The effective resistance of a n number of resistors connected in parallel in x ohm. When one of the resistors is removed, the effective resistance becomes y ohm. The resistance of the resistor that is removed is.... 

(A) {(xy) / (x + y)} 

(B) {(xy) / (y – x)} 

(C) (y – x) 

(D) √xy

Answer 1

The correct option (B) {(xy)/(y – x)}

Explanation:

 effective R when in parallel is x

Hence

(1/R₁) + (1/R₂) + (1/R₃) + --- {1/(R_n–1)} + (1 / R_n) = (1/x) (1)

 if n^th resistor is removed then.

(1/R₁) + (1 / R₂) + ---- {1/(R_n–1)} = (1/y)    (2)

 (1) – (2) gives

(1/R_n) = (1/x) – (1/y)

∴ (1 / R_n) = {(y – x)/(xy)} i.e. R_n = {(xy)/(y – x)}