This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I : Higher the range, greater is the resistance of ammeter.
Statement - II : To increase the range of ammeter, additional shunt needs to be used across it.

First, recall how an ideal ammeter is obtained from a sensitive galvanometer. We begin with a galvanometer coil that has an internal resistance which we shall denote by $$R_g$$ and a full-scale (maximum) current denoted by $$I_g$$. On its own the galvanometer can allow only the current $$I_g$$ to flow without being damaged.

Now suppose we wish to measure a much larger current $$I$$, where $$I > I_g$$. To do so we must send only the current $$I_g$$ through the galvanometer and divert the excess current $$I - I_g$$ through a low-resistance conductor connected in parallel with the galvanometer. This low-resistance conductor is called a shunt and its resistance is written as $$R_s$$.

The galvanometer and the shunt are in parallel, so the potential difference across both is the same. Using Ohm’s law (stated as $$V = IR$$), we write the equality of the two potential drops:

$$I_g \, R_g \;=\; (I - I_g)\, R_s.$$

Solving this expression for the required shunt resistance $$R_s$$, we have

$$R_s \;=\; \frac{I_g\, R_g}{\,I - I_g\,}.$$

Observe the dependence on the desired range $$I$$:

• If we wish to extend the range so that $$I$$ becomes larger, the denominator $$(I - I_g)$$ increases, and hence $$R_s$$ becomes smaller.

Next, let us obtain the effective, or net, resistance of the resulting ammeter. Because the galvanometer (resistance $$R_g$$) and the shunt (resistance $$R_s$$) are in parallel, the equivalent resistance $$R_{\text{A}}$$ of the complete ammeter circuit is given by the parallel-resistance formula, stated as

$$\frac{1}{R_{\text{A}}} \;=\; \frac{1}{R_g} + \frac{1}{R_s},$$

which leads to

$$R_{\text{A}} \;=\; \frac{R_g\, R_s}{\,R_g + R_s\,}.$$

Because $$R_s$$ is chosen to be much smaller than $$R_g$$, the product $$R_g R_s$$ in the numerator is small, and the sum $$R_g + R_s$$ in the denominator is only slightly bigger than $$R_g$$. Consequently the value of $$R_{\text{A}}$$ is smaller than $$R_g$$. As the required measuring range $$I$$ goes higher, we just saw that $$R_s$$ becomes still smaller, and hence $$R_{\text{A}}$$ decreases further.

Therefore, a higher current range for an ammeter is associated with a lower total resistance, not a greater one. This directly contradicts Statement I.

On the other hand, the very method by which we raise the current range is precisely the attachment of a suitable shunt resistance $$R_s$$ in parallel with the galvanometer, which confirms Statement II.

Summarising our findings:

• Statement I: “Higher the range, greater is the resistance of ammeter.”  →  False.
• Statement II: “To increase the range of ammeter, additional shunt needs to be used across it.”  →  True.

Only Statement II is true, so we select the option that states “Statement-I is false, Statement-II is true,” which is Option B.

Hence, the correct answer is Option B.