A galvanometer of resistance 100 Omega, gives a full scale deflection for a current of 10 mA. To convert it into a voltmeter to read 0 to 100 V, the value of the high resistance that should be connected in series with the galvanometer will be

Options

A. `4900 Omega`
B. `9900 Omega`
C. `6000 Omega`
D. `1000 Omega`

Explanation

To solve the problem of converting a galvanometer into a voltmeter, we need to determine the value of the high resistance that should be connected in series with the galvanometer. Here’s a step-by-step solution:

### Step 1: Understand the given values
- Resistance of the galvanometer (Rg) = 100 Ω
- Full-scale deflection current (Ig) = 10 mA = 10 × 10^-3 A
- Desired voltage range for the voltmeter (V) = 100 V

### Step 2: Use the formula for total voltage
When a galvanometer is converted into a voltmeter, the total voltage across the voltmeter (V) is the sum of the voltage across the galvanometer (Vg) and the voltage across the series resistance (Rs). The relationship can be expressed as:
\[ V = I_g \times (R_g + R_s) \]

### Step 3: Rearranging the formula
We can rearrange the formula to find Rs:
\[ R_s = \frac{V}{I_g} - R_g \]

### Step 4: Substitute the known values
Now, substitute the known values into the equation:
- V = 100 V
- Ig = 10 × 10^-3 A
- Rg = 100 Ω

Substituting these values gives:
\[ R_s = \frac{100}{10 \times 10^{-3}} - 100 \]

### Step 5: Calculate Rs
Calculating the first term:
\[ \frac{100}{10 \times 10^{-3}} = \frac{100}{0.01} = 10000 \, \Omega \]

Now substituting this back into the equation for Rs:
\[ R_s = 10000 - 100 = 9900 \, \Omega \]

### Conclusion
The value of the high resistance that should be connected in series with the galvanometer to convert it into a voltmeter reading from 0 to 100 V is **9900 Ω**.

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