A volt-meter of range 2 V and resistance `300 Omega` cannot be converted into ammeter of range:

Options

A. 1 mA
B. 10 mA
C. 1A
D. 100 mA

Explanation

To determine the range of an ammeter that can be converted from a voltmeter with a given resistance, we can follow these steps:

### Step 1: Understand the given data
We have a voltmeter with:
- Range (maximum voltage) = 2 V
- Resistance (R) = 300 Ω

### Step 2: Calculate the current through the voltmeter
The current that can be measured by the voltmeter (which will act as a galvanometer) can be calculated using Ohm's law:

\[ I_g = \frac{V}{R} \]

Substituting the values:

\[ I_g = \frac{2 \, \text{V}}{300 \, \Omega} = \frac{2}{300} = \frac{1}{150} \, \text{A} \approx 6.67 \, \text{mA} \]

### Step 3: Determine the shunt resistance formula
To convert the voltmeter into an ammeter, we need to use a shunt resistor (S). The formula for shunt resistance is given by:

\[ S = \frac{I \cdot I_g}{I - I_g} \]

Where:
- \( I \) = total current through the ammeter
- \( I_g \) = current through the galvanometer (or voltmeter)

### Step 4: Analyze the conditions for conversion
For the conversion to be possible, the shunt resistance \( S \) must be a positive value. This means that the total current \( I \) must be greater than \( 2I_g \):

\[ I > 2I_g \]

Substituting the value of \( I_g \):

\[ I > 2 \times 6.67 \, \text{mA} \approx 13.34 \, \text{mA} \]

### Step 5: Evaluate the possible ranges for the ammeter
Now we evaluate the possible ranges for the ammeter:
1. 1 mA
2. 10 mA
3. 1 A

- For **1 mA**: \( 1 \, \text{mA} < 13.34 \, \text{mA} \) (not possible)
- For **10 mA**: \( 10 \, \text{mA} < 13.34 \, \text{mA} \) (not possible)
- For **1 A**: \( 1000 \, \text{mA} > 13.34 \, \text{mA} \) (possible)

### Conclusion
The voltmeter cannot be converted into an ammeter for ranges of **1 mA** and **10 mA** since both are less than the required \( 13.34 \, \text{mA} \).