Question

An ammeter is obtained by shunting a 30 $\Omega$ galvanometer with a 30$\Omega$ resistance. What additional shunt should be connected across it to double the range?

• A. 15 $\Omega$
• B. 10 $\Omega$
• C. 5 $\Omega$
• D. none of these

Answer 1

The correct option is A 15 $\Omega$

Initially, $S=\frac{i_g}{I-i_g}G$

$30=\frac{i_g}{I-i_g}\times 30\Rightarrow I=2i_g$

When range is doubled i.e $I^{\prime }=2I=4i_g$
Now shunt required is: $S^{\prime }=\frac{i_g}{I^{\prime }-i_g}G=\frac{i_g}{4i_g-i_g}\times 30=10\Omega$

As shunt is connected in parallel to galvanometer, if additional shunt $x$ then
$30||x=10$ or $\frac{30x}{30+x}=10$

$30+x=3x\Rightarrow x=15\Omega$