The error in measuring the current with a tangent galvanometer is… - Vidyadip

MCQ

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

A
$0^\circ$
B
$30^\circ$
✓
$45^\circ$
D
$60^\circ$

✓

Answer

Correct option: C.

$45^\circ$

In case of tangent galvanometer as$i=k \tan \phi$Differentiating both side w.r.t. $\phi$
$ \frac{d i}{d \phi}=k \sec ^2 \phi \Rightarrow d i=k \sec ^2 d \phi $
$ \Rightarrow \frac{d i}{i}=\frac{d \phi}{\sin \phi \cos \phi}=\frac{2 d \phi}{\sin 2 \phi}$
Hence the error in the measurement will be least when
$\sin 2 \phi=\max =1 \Rightarrow 2 \phi=90^{\circ} \Rightarrow \phi=45^{\circ}$

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