Question

The range of an ammeter of resistance G, is increased from I to nI. This can be done connecting

• A. a series resistance of Gn
• B. a parallel resistance of G/(n - 1)
• C. a series resistance of G (n - 1)
• D. a parallel resistance of G/n

Answer 1

Answer: (B)

a parallel resistance of G/(n - 1)

Answer 2

For a galvanometer of resistance $G$ and full-scale current $I$, to increase the range to $nI$, we connect a shunt resistor $R_{sh}$ in parallel. The galvanometer will still carry $I$ while the shunt carries $(n-1)I$. Equate the voltage drops across them:

$$I \times G = (n-1)I \times R_{sh}$$

Cancel $I$ (assuming $I \neq 0$):

$$G = (n-1)R_{sh} \quad\Longrightarrow\quad R_{sh} = \frac{G}{n-1}$$

Thus, we must connect a parallel resistance of $\frac{G}{(n-1)}$.