Question

A galvanometer is shunted by (1/n)${}^{th}$ of its resistance . The fraction of the total current passing through the galvanometer is:

• A. 1/(1+n)
• B. n/(1+n)
• C. 1/n
• D. 1/(n-1)

Answer 1

The correct option is A 1/(1+n)

Let the total current be $1A$.

Let the current through galvanometer be $I_g$

Let the galvanometer resistance be $R_g$

Let the shunt resistance be $R_s$

$R_s=\frac{R_g}{n}$

$R_s=\frac{I_g}{1-I_g}{R}_g⟹\frac{R_g}{n}=\frac{I_g}{1-I_g}{R}_g$

$⟹\frac{1}{n}=\frac{I_g}{1-I_g}⟹n{I}_g=1-I_g$

$⟹n{I}_g+I_g=1$

$⟹(n+1)I_g=1$

$\therefore I_g=\frac{1}{n+1}$