A galvanometer of resistance `25 Omega` gives full scale deflection for a current of 10 milliampere , is to be changed into a voltmeter of range 100 V by connecting a resistance of ‘ R ’ in series with galvanometer. The value of resistance R in `Omega` is

Options

A. 10000
B. 975
C. 10025
D. 9975

Answer

To solve the problem of converting a galvanometer into a voltmeter, we need to follow these steps:

### Step 1: Understand the given values
- The resistance of the galvanometer (Rg) = 25 Ω
- The full-scale deflection current (Ig) = 10 mA = 10 × 10^(-3) A
- The desired voltage range for the voltmeter (V) = 100 V

### Step 2: Set up the equation for the total voltage
When the galvanometer is connected in series with a resistance (R), the total voltage across the combination when the full-scale deflection current is flowing can be expressed as:
\[ V = I_g \times (R_g + R) \]
Where:
- V = total voltage (100 V)
- Ig = full-scale deflection current (10 × 10^(-3) A)
- Rg = resistance of the galvanometer (25 Ω)
- R = resistance to be calculated

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 100 = (10 \times 10^{-3}) \times (25 + R) \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 100 = 0.01 \times (25 + R) \]

### Step 5: Solve for (25 + R)
To isolate (25 + R), divide both sides by 0.01:
\[ 100 / 0.01 = 25 + R \]
\[ 10000 = 25 + R \]

### Step 6: Solve for R
Now, subtract 25 from both sides to find R:
\[ R = 10000 - 25 \]
\[ R = 9975 \, \Omega \]

### Conclusion
The value of the resistance R that needs to be connected in series with the galvanometer to convert it into a voltmeter of range 100 V is **9975 Ω**.

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