The error in measuring the curent with tangent galvanometer is minimum when the deflection is about

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

C

Explanation

In case of tangent galvanometer as
`i=k tan varphi`
Differentiating both side w.r.t. `varphi`
`(di)/(d varphi)=k sec^(2) varphiimplies di=k sec^(2) d varphi`
`implies (di)/i=(d varphi)/(sin varphi cos varphi)=(2dvatphi)/(sin2varphi)`
Hence, the error in the measurement will be least when
`sin 2 varphi=max=1implies2 "varphi=90^(@)implies varphi=45^(@)`