Question

If a shunt of $\frac{1}{10}$th of the coil resistance is applied to a moving coil galvanometer, its sensitivity becomes:

• A. $10$ fold
• B. $\frac{1}{10}$ fold
• C. $11$ fold
• D. $\frac{1}{11}$ fold

Answer 1

The correct option is D $\frac{1}{11}$ fold

Given $R_s=\frac{R_g}{10}$

$R_g||R_s=\frac{R_g{R}_s}{R_g+R_s}$

$=\frac{R_g}{11}$

Let voltage across galvanometer be $V$

$V=I_g{R}_g=I\left(R_g||R_s\right)$

$I_g{R}_g=\frac{I{R}_g}{11}$

$I_g=\frac{I}{11}$

Adding a shunt in parallel increases the range but reduces the sensitivity.

Sensitivity is defined as the ratio of deflection and current measured.

Original sensitivity is $S_i=\frac{\theta }{I_g}$

New sensitivity is $S_f=\frac{\theta }{I}=\frac{\theta }{11I_g}$

$\frac{S_f}{S_i}=\frac{1}{11}$