Question

The deflection in galvanometer falls to $[\frac{1}{4}{]}^{th}$ when it is shunted by 3$\Omega$. If additional shunt of $2\Omega$ is connected to earlier shunt, the deflection in galvanometer falls to

• A. $\frac{1}{2}$
• B. ${\frac{1}{3}}^{rd}$
• C. ${\frac{1}{4}}^{th}$
• D. ${\frac{1}{8.5}}^{th}$

Answer 1

The correct option is D ${\frac{1}{8.5}}^{th}$

The current through the galvanometer is given by

$i_1=\frac{R_s}{R_s+R_g}i$ where $R_s$=resistance of shunt and $R_g$=resistance of galvanometer

In the first case:-

$I_1=\frac{3}{3+R_g}i=\frac{i}{4}$

$⟹R_g=9\Omega$

Now, when an extra of $2\Omega$ is shunted means the parallel combination of $2\Omega$ and $3\Omega$ will be the $R_s$

$⟹R_s=\frac{2\times 3}{2+3}=1.2\Omega$

$i_1=\frac{1.2}{1.2+9}i=\frac{1.2}{10.2}i$

$⟹i_1=\frac{1}{8.5}i$

Hence, the answer is option-(D).