The range of voltmeter of resistance `300 Omega` is 5 V. The resistance to be connected to convert it into an ammeter of range 5 A is

Options

A. ` 1 Omega "in series"`
B. `1 Omega "in parallel"`
C. `0.1 Omega "in series"`
D. `0.1 Omega "in parallel"`

Explanation

To convert a voltmeter into an ammeter, we need to connect a shunt resistance in parallel with the galvanometer. Let's solve the problem step by step.

### Step 1: Understand the given data
- The resistance of the voltmeter (which is the same as the galvanometer resistance, G) = 300 Ω
- The range of the voltmeter = 5 V
- The desired range of the ammeter = 5 A

### Step 2: Calculate the current through the galvanometer (Ig)
Using Ohm's Law, we can find the current that corresponds to the full-scale deflection of the voltmeter (Ig):

\[ I_G = \frac{V}{R} = \frac{5 \, \text{V}}{300 \, \Omega} = \frac{1}{60} \, \text{A} \]

### Step 3: Use the formula for shunt resistance (S)
The formula for calculating the shunt resistance (S) needed to convert the galvanometer into an ammeter is given by:

\[ S = \frac{I_G \cdot G}{I - I_G} \]

Where:
- \(I_G\) = current through the galvanometer = \(\frac{1}{60} \, \text{A}\)
- \(G\) = resistance of the galvanometer = 300 Ω
- \(I\) = total current for the ammeter = 5 A

### Step 4: Substitute the values into the formula
Now, substituting the values into the formula:

\[ S = \frac{\left(\frac{1}{60}\right) \cdot 300}{5 - \left(\frac{1}{60}\right)} \]

### Step 5: Simplify the expression
First, calculate the denominator:

\[ 5 - \frac{1}{60} = \frac{300}{60} - \frac{1}{60} = \frac{299}{60} \]

Now substitute back into the formula for S:

\[ S = \frac{\left(\frac{1}{60}\right) \cdot 300}{\frac{299}{60}} = \frac{300}{299} \]

### Step 6: Calculate the value of S
Now, simplifying further:

\[ S = \frac{300}{299} \approx 1.003 \, \Omega \]

Since we need a small resistance, we can round this to 1 Ω.

### Conclusion
The resistance to be connected to convert the voltmeter into an ammeter of range 5 A is approximately **1 Ω**.

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