Question

The coil in a moving coil galvanometer has an area of $4{\text{cm}}^2$ and $500$ turns. The magnetic induction field is $2\text{T}$ when a current of ${10}^{-4}\text{A}$ is passed through it, the deflection is ${20}^{\circ }$. The couple per unit twist in $\text{Nm}{\text{degree}}^{-1}$ is

• A. $1\times {10}^{-6}$
• B. $4\times {10}^{-6}$
  
• C. $6\times {10}^{-6}$
  
• D. $2\times {10}^{-6}$

Answer 1

The correct option is D $2\times {10}^{-6}$

Given, $N=500;A=4{\text{cm}}^2;B=2\text{T}I={10}^{-4}\text{A};\theta ={20}^{\circ }$

Deflection of the coil is $\propto$ Torque acting it.

$NIAB\propto \theta$

$NIAB=C\theta$

$C=\frac{NIAB}{\theta }=\frac{2\times {10}^{-4}\times 4\times {10}^{-4}\times 500}{{20}^0}$

$\therefore C=2\times {10}^{-6}\text{Nm}{\text{degree}}^{-1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.