Question

A moving-coil galvanometer has $100\text{turns}$ and each turn has an area $2.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.01\text{T}$. The deflection in the coil is $0.05\text{radian}$ when a current of $10\text{mA}$ is passed through it. Find the torsional constant of the suspension wire.

• A. $2.0\times {10}^{-5}\text{Nm/rad}$
• B. $4.0\times {10}^{-5}\text{Nm/rad}$
• C. $3.0\times {10}^{-5}\text{Nm/rad}$
• D. $1.0\times {10}^{-5}\text{Nm/rad}$

Answer 1

The correct option is B $4.0\times {10}^{-5}\text{Nm/rad}$

Given:

Number of turns, $N=100$

Area of each turn, $A=2.0{\text{cm}}^2=2\times {10}^{-4}{\text{m}}^2$

Magnetic field, $B=0.01\text{T}$

Current passing through the coil, $I=10\text{mA}=10\times {10}^{-3}\text{A}$

Deflection in the coil, $\varphi =0.05\text{rad}$

The torsional constant of a wire used in a moving coil galvanometer is,

$C=\frac{NIBA}{\varphi }$

Substituting the values,

$C=\frac{\left(100\right)\times (10\times {10}^{-3})\times \left(0.01\right)\times (2\times {10}^{-4})}{0.05}$

$=4.0\times {10}^{-5}\text{Nm/rad}$

Hence, option $\left(A\right)$ is the correct answer.