Question

The deflection in a galvanometer falls from $50$ divisions to $20$ divisions, when a $12\Omega$ shunt (resistance connected in parallel to galvanometer) is applied. The galvanometer resistance is

• A. $18\Omega$
• B. $24\Omega$
• C. $30\Omega$
• D. $36\Omega$

Answer 1

The correct option is A $18\Omega$

We know that a shunt resistance is connected in parallel to galvanometer as shown below. Let $S$ and $G$ be the resistance of shunt and galvanometer respectively.


From diagram,

$\frac{I_G}{I_S}=\frac{S}{G}$

$\Rightarrow G=\frac{I_S}{I_G}\times S$

$\Rightarrow G=\frac{50-20}{20}\times 12$

$[\because I_G=20k\text{and}{I}_S=50k-20k=30k\text{where,}k\text{is proportionality constant}]$

$\therefore G=18\Omega$

Hence, option $\left(a\right)$ is correct.
$$\begin{array}{c}\text{Why this question ?}\\ \text{Concept-For any galvanometer, angle}\\ \text{of deflection}\theta \text{is proportional to the}\\ \text{amount of current (i) flowing through it.}\\ \therefore i=k\theta \end{array}$$