Question

A Galvanometer of resistance $G$ is to be converted into ammeter, with the help of a shunt resistance $S.$ If the ratio of heat dissipated through galvanometer and shunt is $3:4$ then

• A. $G=\frac{9}{16}S$
• B. $G=\frac{16}{9}S$
• C. $S=\frac{4}{3}G$
• D. $S=\frac{3}{4}G$

Answer 1

The correct option is D $S=\frac{3}{4}G$

Let, heat dissipated across the galvanometer $G$ and Shunt resistance $S$ be $Q_G$ and $Q_S$respectively.


$Q_G=i_g^{2}Gt=\frac{V^2}{G^2}\times Gt$

$\therefore Q_G=\frac{V^{2}t}{G}......\left(1\right)$

Similarly,

$Q_S=i_s^{2}St=\frac{V^2}{S^2}\times St$

$\therefore Q_S=\frac{V^{2}t}{S}......\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ we get,

$\frac{Q_G}{Q_S}=\frac{S}{G}$

$\Rightarrow \frac{3}{4}=\frac{S}{G}$

$\therefore S=\frac{3}{4}G$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.