Question
The error in measuring the current with a tangent galvanometer is minimum when the deflection is about.....$^o$
✓
Answer
(c)In case of tangent galvanometer as
$i = k\tan \phi $
Differentiating both side w.r.t. $\phi $
$\frac{{di}}{{d\phi }} = k{\sec ^2}\phi \Rightarrow di = k{\sec ^2}d\phi $
$ \Rightarrow \frac{{di}}{i} = \frac{{d\phi }}{{\sin \phi \cos \phi }} = \frac{{2d\phi }}{{\sin 2\phi }}$
Hence the error in the measurement will be least when
$\sin 2\phi = \max = 1$$ \Rightarrow 2\phi = {90^o} \Rightarrow \phi = {45^o}$
$i = k\tan \phi $
Differentiating both side w.r.t. $\phi $
$\frac{{di}}{{d\phi }} = k{\sec ^2}\phi \Rightarrow di = k{\sec ^2}d\phi $
$ \Rightarrow \frac{{di}}{i} = \frac{{d\phi }}{{\sin \phi \cos \phi }} = \frac{{2d\phi }}{{\sin 2\phi }}$
Hence the error in the measurement will be least when
$\sin 2\phi = \max = 1$$ \Rightarrow 2\phi = {90^o} \Rightarrow \phi = {45^o}$
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