A galvanometer having a resistance of `50Omega` , gives a full scale deflection for a current if `0.05` A. The length in metre if a resistance wire of area of cross- section `2.97 xx10^-2cm^2` that can be used to convert the gaivanometer into an ammeter which can read a maximum of 5 A current is (specific resistance of the wire =`5xx10^-7Omega-m`)

Options

A. 9
B. 6
C. 3
D. `1.5`

Answer

B

Explanation

Three unequal resistance are in parallel
`(1)/(R_(eq)) = (1)/(R_1)+(1)/(R_2)+ (1)/(R_3)`
Here , `R_(eq) = 1Omega and (R_1)/(R_2) =(1)/(2) (1)/(1) = (1)/(R_1)+(1)/(2R_1) +(1)(R_3)`
Rightarrow `(1)/(1) = (3)/(2R_1) + (1)/(R_3)`
Rightarrow `1- (3)/(2R_1)= (1)/(R_3)`
`(2R_1-3)/(2R_1)=(1)/(R_3)`
`R_3 = (2R_1)/(2R_1-3)`
`R_1= 3`, Satisfies the above condtions
therefore `R_1= 3, R_2= 6, R_3= (2(3))/(6-3)= (6)/(3) = 2`
therefore The largest of the three resistance is , `R_2= 6Omega`