Question

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

• A. $0^0$
• B. ${60}^0$
• C. ${30}^0$
• D. ${45}^0$

Answer 1

The correct option is D ${45}^0$

For a tangent galvanometer, if deflection $=\varphi$, then the current reading is given by

$i=ktan\varphi$ .....(i)

Where, reduction factor of galvanometer

$k=\frac{2r{B}_H}{{\mu }_{0}n}=constant$

Differentiating both sides of (i) we get,

$di=kse{c}^2\varphi d\varphi$

$\Rightarrow \frac{di}{i}=\frac{kse{c}^2\varphi d\varphi }{ktan\varphi }$


$\Rightarrow \frac{di}{i}=\frac{d\varphi }{sin\varphi cos\varphi }$

$\Rightarrow \frac{di}{i}=\frac{2d\varphi }{sin2\varphi }$

Thus, error will be minimum when,

$\Rightarrow 2\varphi ={90}^0$

$\Rightarrow \varphi ={45}^0$

Hence, the correct option is (C)