Question

When a galvanometer is shunted with a $4\Omega$ resistance, the deflection is reduced to one - fifth. If the galvanometer is further shunted with a $2\Omega$ wire, determine current in galvanometer now if initially current in galvanometer is $I_0$ (given main current remain same).

• A. $I_0/13$
• B. $I_0/5$
• C. $I_0/8$
• D. $5I_0/13$

Answer 1

The correct option is A $I_0/13$

Given: When a galvanometer is shunted with a $4\Omega$ resistance, the deflection is reduced to one - fifth. Also initially current in galvanometer is $I_0$

To find the current in galvanometer if the galvanometer is further shunted with a $2\Omega$ wire

Solution:

When shunted with resistance of $4\Omega$, we get

$\frac{I_0}{5}\times R_g=\frac{4I_0}{5}\times 4$, as given initial current is $I_0$ and$R_g$ is shunt resistance

$⟹R_g=16\Omega$

When further shunted with $2\Omega$ resistance, we get

$I^{\prime }\times 16=(I_0-I^{\prime })\times \frac{4}{3}$, where $I^{\prime }$ is the required current after further shunting

$⟹12I^{\prime }=I_0-I^{\prime }⟹I^{\prime }=\frac{I}{13}$

is the required current.