In the labortary, the high emf of a battery is measured by using potentiometer and two resistance `R_(1)` and `R_(2)`, where `R_(1) lt lt R_(2)` as shown in the figure
`R_(1)=(100+-0.10)Omega` and `R_(2)=(9900+-9.90)Omega`, `AB=1m` The voltage across `R_(1)`, when switches `S_(1)` & `S_(2)` are connected to point `1` and point `2` is balanced against `l_(1)=(60+-0.06)cm`. when the switches `S_(1)` and `S_(2)` are shifted to point `3` and point `4` as shown in the figure, the potential difference of standard `E_(0)=2` volt is balanced against length `l_(2)=(75+-0.075)cm`. The maximum error in emf of battery `E` is __________ volts (upto two decimal places)

Explanation

`E=2xx(60)/(75)xx((10000)/(100))=160` volt , `E=E_(0)(l_(1))/(l_(2))((R_(1)+R_(2))/(R_(1)))`
`(DeltaE)/(E)=|(Deltal_(1))/(l_(1))|+|(Deltal_(2))/(l_(2))|+|(Delta(R_(1)+R_(2)))/(R_(1)+R_(2))|+|(DeltaR_(1))/(R_(1))|`
`rArr DeltaE=0.64` volts