A galvanometer having internal resistance `10 Omega` required `0.01` A for a full scale deflection. To convert this galvanometer to a voltmeter of full scale deflection at 120 V, we need to connect a resistance of

Options

A. `11990 ` `Omega` in series
B. `11990 Omega` in parallel
C. `12010 Omega` in series
D. `12010 Omega` in parallel

Answer

To convert a galvanometer into a voltmeter, we need to calculate the resistance that should be connected in series with the galvanometer. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Internal resistance of the galvanometer, \( R_g = 10 \, \Omega \)
- Full scale deflection current of the galvanometer, \( I_g = 0.01 \, A \)
- Full scale deflection voltage for the voltmeter, \( V = 120 \, V \)

### Step 2: Use the formula for the series resistance
To convert the galvanometer into a voltmeter, we use the formula:
\[ R = \frac{V}{I_g} - R_g \]
where \( R \) is the resistance to be connected in series, \( V \) is the voltage for full scale deflection, \( I_g \) is the current for full scale deflection through the galvanometer, and \( R_g \) is the internal resistance of the galvanometer.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ R = \frac{120 \, V}{0.01 \, A} - 10 \, \Omega \]

### Step 4: Calculate \( \frac{120}{0.01} \)
Calculating the first part:
\[ \frac{120}{0.01} = 12000 \, \Omega \]

### Step 5: Subtract the internal resistance of the galvanometer
Now, subtract the internal resistance of the galvanometer:
\[ R = 12000 \, \Omega - 10 \, \Omega = 11990 \, \Omega \]

### Step 6: Conclusion
The resistance that needs to be connected in series with the galvanometer to convert it into a voltmeter with a full scale deflection of 120 V is:
\[ R = 11990 \, \Omega \]