A galvanometer of resistance `30Omega` is connected to a battery of emf 2 V with `1970Omega` resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is

Options

A. `4030Omega`
B. `4000Omega`
C. `3970Omega`
D. `2000Omega`

Answer

C

Explanation

`I_(1)=I_(2)" ":'theta_(1)=theta_(2)`
`(V)/(G+R_(1))=(V)/(G+R_(2))" ":.thetapropI`
`i.e., thetaprop(1)/(V)`
`(10)/(30+1970)=(20)/(30+R_(2))`
`(10)/(2000)=(20)/(30+R_(2))`
`4000=30+R_(2)`
`:.R_(2)=4000=30+R_(2)`
`:.R_(2)=4000-30`
`=3970Omega`