Four resistors A, and D form a Wheatstone bridge.
The bridge is balanced , when C = `100Omega` If A and B are interchanged the bridge balances for `C=121Omega`. The value of D is

Options

A. `10Omega`
B. `100Omega`
C. `110Omega`
D. `120Omega`

Answer

A

Explanation

(1) Equivalent Resistance `R=R_1+R_2+=R+R+R=3R`
Power dissipation , `p= i^2R= i^2(3R) = 3i^2R`
(ii) `R_eq = (2RxxR)/(2R+R) = (2R^2)/(3R)= (2R)/(3)`
`p=i^2R=i^2((2R/3))=(2)/(3)i^2i^2R `
(iii)`R_(eq)==(((R)/(2))R)/(R/2+R )= (R^2)/(2)xx(2)/(3R)=(R)/(3)`
`P= i^2R =i^2 ((R)/(3))= (1)/(3)i^2R`
(iv) `R_eq = (3)/(2)ROmega`
`P= i^2R=i^2((3)/(2)R))= (3)/(2)i^2R`
`therefore` option (a) has more power dissipation .