Magnetism Question 121
Question: The error in measuring the current with a tangent galvanometer is minimum when the deflection is about
[MP PET 2001]
Options:
A) 0o
B) 30o
C) 45o
D) 60o
Show Answer
Answer:
Correct Answer: C
Solution:
In case of tangent galvanometer as $ i=k\tan \varphi $ Differentiating both side w.r.t. $ \varphi $
$ \frac{di}{d\varphi }=k{{\sec }^{2}}\varphi \Rightarrow di=k{{\sec }^{2}}d\varphi $
$ \Rightarrow \frac{di}{i}=\frac{d\varphi }{\sin \varphi \cos \varphi }=\frac{2d\varphi }{\sin 2\varphi } $ Hence the error in the measurement will be least when $ \sin 2\varphi =\max =1 $
$ \Rightarrow 2\varphi =90^{o}\Rightarrow \varphi =45^{o} $
BETA
