Question

For what value of angular deflection, the instrument is most accurate

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

Answer 1

Answer: (C)

45°

Answer 2

For a tangent galvanometer, the current is given by

$$I \propto \tan \theta$$

A small error in measuring $\theta$ results in an error in $I$. Differentiating, we find

$$\frac{dI}{I} = \frac{d\theta}{\sin\theta \cos\theta} = \frac{2\,d\theta}{\sin 2\theta}$$

To minimize the relative error $\frac{dI}{I}$, maximize $\sin 2\theta$. The maximum value of $\sin 2\theta$ is 1, which occurs when

$$2\theta = 90^\circ \quad \Longrightarrow \quad \theta=45^\circ.$$