Question

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

• A. (a) 0°
• A. (b) 30°
• A. (c) 45°
• A. (d) 60°

Answer 1

(c)

Sol. 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

$\sin 2 \phi = \max = 1$ $\Rightarrow 2 \phi = 90 ^ { \circ } \Rightarrow \phi = 45 ^ { \circ }$