The scale of a galvanometer of resistance `100 ohms` contains 25 divisions. It gives a defelction of one division on passing a current of `4xx 10 ^(-4)` amperes. The resistance in ohms to be added to it, so that it may become a voltmeter of range `2.5` volts is

Options

A. 100
B. 150
C. 250
D. 300

Explanation

To solve the problem step by step, we need to determine the resistance that should be added to the galvanometer to convert it into a voltmeter with a range of 2.5 volts.

### Step 1: Calculate the total current through the galvanometer (Ig)
The galvanometer gives a deflection of one division for a current of \(4 \times 10^{-4}\) A. Since there are 25 divisions, the total current \(I_g\) when the galvanometer is fully deflected would be:
\[ I_g = 25 \times (4 \times 10^{-4}) = 1 \times 10^{-2} \text{ A} = 0.01 \text{ A} \]

### Step 2: Identify the resistance of the galvanometer (G)
The resistance of the galvanometer is given as:
\[ G = 100 \text{ ohms} \]

### Step 3: Use the formula for the resistance to be added (R)
To convert the galvanometer into a voltmeter, we can use the formula:
\[ R = \frac{V}{I_g} - G \]
where \(V\) is the desired voltage range of the voltmeter (2.5 V).

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ R = \frac{2.5}{0.01} - 100 \]

### Step 5: Calculate the value of R
Calculating the first part:
\[ \frac{2.5}{0.01} = 250 \]
Now substituting back into the equation:
\[ R = 250 - 100 = 150 \text{ ohms} \]

### Conclusion
The resistance that needs to be added to the galvanometer to convert it into a voltmeter with a range of 2.5 volts is:
\[ \boxed{150 \text{ ohms}} \]

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