1. Given data

• Full scale deflection current of galvanometer: $I_g = 5\text{ mA} = 5 \times 10^{-3}\text{ A}$
• Resistance of galvanometer coil: $G = 15\,\Omega$
• Desired voltmeter range: $V = 10\text{ V}$

2. Condition for converting galvanometer into voltmeter

To convert a galvanometer into a voltmeter of range $0$ to $10\,$V, a high resistance $R$ is connected in series with the galvanometer.

At full scale deflection, the galvanometer current is $I_g$, so: $V = I_g(G + R)$

3. Substitute the values

$10 = 5 \times 10^{-3}(15 + R)$

4. Solve for $R$

$15 + R = \frac{10}{5 \times 10^{-3}} = 2000$

So, $R = 2000 - 15 = 1985\,\Omega$

5. Write in scientific notation

$R = 1.985 \times 10^3\,\Omega$

6. Match with the options

This corresponds to:

Option B: $1.985 \times 10^3\,\Omega$

7. Comparison with stored correct answer

Stored correct answer is B, which matches our derived answer.