A glavanometer of `50 Omega` resistance has 25 divisions. A current of `4xx10^(-4)` A gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of `25 V`, it should be connected with a resistance of

Options

A. 245 `Omega` as a shunt
B. 2550 `Omega` in series
C. 2450 `Omega` in series
D. 2500 `Omega` as a shunt

Explanation

To convert the galvanometer into a voltmeter with a range of 25 V, we need to follow these steps:

### Step 1: Determine the current corresponding to full-scale deflection
Given that a current of \(4 \times 10^{-4}\) A gives a deflection of one division and the galvanometer has 25 divisions, we can find the total current that corresponds to full-scale deflection:

\[ I_G = 4 \times 10^{-4} \, \text{A} \times 25 = 10^{-2} \, \text{A} \]

### Step 2: Calculate the total resistance required for the voltmeter
To find the total resistance \(R_T\) needed for the voltmeter, we can use Ohm's law, where voltage \(V\) is equal to current \(I\) multiplied by resistance \(R\):

\[ R_T = \frac{V}{I_G} = \frac{25 \, \text{V}}{10^{-2} \, \text{A}} = 2500 \, \Omega \]

### Step 3: Calculate the resistance in series
The total resistance of the voltmeter is the sum of the galvanometer's resistance \(R_G\) and the series resistance \(R_S\):

\[ R_T = R_G + R_S \]

Given that the resistance of the galvanometer \(R_G\) is 50 Ω, we can rearrange the equation to find \(R_S\):

\[ R_S = R_T - R_G = 2500 \, \Omega - 50 \, \Omega = 2450 \, \Omega \]

### Conclusion
To convert the galvanometer into a voltmeter with a range of 25 V, a resistance of **2450 Ω** should be connected in series.

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