The scale of a galvanometer of resistance 100 ohms contains 25 divisions. It gives a deflection of one division on passing a current of` 4 xx 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, we need to determine the resistance that should be added to a galvanometer to convert it into a voltmeter with a specified range. Here’s the step-by-step solution:

### Step 1: Understand the given values
- Resistance of the galvanometer (G) = 100 ohms
- Current for 1 division deflection (Ig) = 4 x 10^(-4) A
- Voltage range (V) = 2.5 V
- Number of divisions on the galvanometer scale = 25

### Step 2: Calculate the voltage corresponding to a deflection of 1 division
The voltage across the galvanometer when it shows a deflection of 1 division can be calculated using Ohm's Law:
\[ V_g = I_g \times G \]
Substituting the known values:
\[ V_g = (4 \times 10^{-4}) \times 100 \]
\[ V_g = 4 \times 10^{-2} \text{ V} = 0.04 \text{ V} \]

### Step 3: Determine the total resistance needed for the voltmeter
To convert the galvanometer into a voltmeter, we need to find the total resistance (R_total) that will allow it to measure up to 2.5 V. The formula for the total voltage in terms of the galvanometer current and the additional resistance (R) is:
\[ V = I_g \times (G + R) \]
Rearranging the formula to find R:
\[ R = \frac{V}{I_g} - G \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have into the equation:
\[ R = \frac{2.5}{4 \times 10^{-4}} - 100 \]

### Step 5: Calculate R
Calculating the first term:
\[ \frac{2.5}{4 \times 10^{-4}} = \frac{2.5}{0.0004} = 6250 \text{ ohms} \]

Now, substituting this back into the equation for R:
\[ R = 6250 - 100 \]
\[ R = 6150 \text{ ohms} \]

### Step 6: Conclusion
The resistance to be added to the galvanometer to convert it into a voltmeter of range 2.5 volts is **6150 ohms**.

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