Two tangent galvanometer have redii `7.5 cm` and `10 cm`, number of turns are 15 and 10 and resistances are `8 Omega` and `12 Omega`. They are joined in parallel in circuit. If deflection in one is `60^(@)` the deflection in second galvanometer is :

Options

A. `45^(@)`
B. `30^(@)`
C. `40^(@)`
D. `35^(@)`

Answer

B

Explanation

`r_(1)=7.5 cm, r_(2)=10cm`
`n_(1)=15, n_(2)=10`
`R_(1)=8, R_(2)=12`
`theta_(1)=60^(@), theta_(2)=?`
`m_(0)/2n_(1)/r_(1)xxI_(1)=tantheta_(1)`
`mu_(0)/2n_(2)/r_(2)xxI_(2)=tantheta_(2)`
`:. (tantheta_(2))/(tantheta_(1))=n_(2)/n_(1)xxr_(1)/r_(2)xxI_(2)/I_(1)`
But `I_(1)=R_(2)/(R_(1)+R_(2))xxV/R_(p)`
`I_(2)=R_(2)/(R_(1)+R_(2))xxV/R_(p)`
`I_(2)/I_(1)=R_(1)/R_(2)`
From equation (iii),
`(tantheta_(2))/(tantheta_(1))=10/15xx75/10xx8/12=1/3`
`:. tantheta_(2)=sqrt(3)/3=1/sqrt(3)`
`:. theta_(2)=30^(@)`