Question

A galvanometer is shunted by $\frac{1}{r}$ of its resistance. Find the fraction of total current passing through the galvanometer.

Answer 1

Galvanometer resistance $R_g=r$

Shunt resistance $R_s=\frac{1}{r}$

Using $I=I_g(1+\frac{R_g}{R_s})$

So, fraction of total current passing through galvanometer $\frac{I_g}{I}=\frac{R_s}{R_s+R_g}$

$⟹\frac{I_g}{I}=\frac{1/r}{\left(1/r\right)+r}=\frac{1}{1+r^2}$