Question

A galvanometer has a resistance of $3663\omega$. A shunt S is connected across it such that $\frac{1}{34}$ of the total current passes through the galvanometer. The value of the shunt is

Answer 1

Step 1: Given data

A galvanometer has a resistance of $G=3663\omega$.

A shunt S is connected across it such that $\frac{1}{34}$ of the total current passes through the galvanometer.

Step 2: Formula used

A shunt $S$ is connected in parallel with a galvanometer with resistance $G$ , then we know that the current in the circuit gets divided. If $i$ is the total current in the circuit and $i_g$ is the current in the galvanometer, then the current flowing through the shunt resistance is given as $i_s=i-i_g$

$\frac{S}{G}=\frac{i_g}{i-i_g}$

Step 3: Calculating the value of the shunt

Given that the $i_g=\frac{i}{34}$
Since the voltage in both circuit are equal, we also know from the ohms law that $V=IR$.

Applying the same, we $\frac{S}{G}=\frac{i_g}{i-i_g}$
Also, given that the $G=3663\omega$

Substituting the values, we get, $S=\frac{{\displaystyle \frac{i}{34}}}{i-{\displaystyle \frac{i}{34}}}\times G$

$⟹S=\frac{G}{33}=\frac{3663}{33}=111\omega$

Hence, the value of the shunt is $111\omega$.