Question

An ammeter is designed by shunting $12\Omega$ galvanometer with $6\Omega$ resistance, the additional shunt that should be connected across it to quadruple the range is

• A. $4\Omega$
• B. $3\Omega$
• C. $\frac{4}{3}\Omega$
• D. $\frac{3}{4}\Omega$

Answer 1

The correct option is C $\frac{4}{3}\Omega$

The resistance of galvanometer after shunting $12\Omega$ resistance:
$G=\frac{12\times 6}{12+6}=4\Omega$

Now, as we connect one more shunt $S$, the range becomes four times the first. The formula for shunt $S$ to increase the range by $n$ times is given by:
$S=\frac{G}{n-1}\Rightarrow S=\frac{4}{4-1}=\frac{4}{3}\Omega$