100mA current gives a full scale deflection in a galvanometer of `2Omega` resistance. The resistance connected with the galvanometer to convert it into a voltmeter to measure 5V is

Options

A. `98 Omega`
B. `52 Omega`
C. `50 Omega`
D. `48 Omega`

Answer

To solve the problem of finding the resistance \( R_s \) that needs to be connected in series with a galvanometer to convert it into a voltmeter capable of measuring 5V, we can follow these steps:

### Step 1: Understand the Circuit Configuration
We need to connect a resistance \( R_s \) in series with the galvanometer. The total voltage across the circuit will be the sum of the voltage across the galvanometer and the voltage across the series resistance.

### Step 2: Identify Given Values
- Full-scale deflection current \( I_s = 100 \, \text{mA} = 100 \times 10^{-3} \, \text{A} = 0.1 \, \text{A} \)
- Resistance of the galvanometer \( G = 2 \, \Omega \)
- Voltage to be measured \( V = 5 \, \text{V} \)

### Step 3: Use Ohm's Law
The voltage across the entire circuit can be expressed as:
\[ V = I_s \times (R_s + G) \]
Where:
- \( R_s \) is the resistance we need to find,
- \( G \) is the resistance of the galvanometer.

### Step 4: Rearrange the Equation
We can rearrange the equation to solve for \( R_s \):
\[ R_s = \frac{V}{I_s} - G \]

### Step 5: Substitute the Known Values
Now, substitute the known values into the equation:
\[ R_s = \frac{5 \, \text{V}}{0.1 \, \text{A}} - 2 \, \Omega \]

### Step 6: Calculate \( R_s \)
Calculating the first part:
\[ \frac{5}{0.1} = 50 \, \Omega \]
Now, substituting back into the equation:
\[ R_s = 50 \, \Omega - 2 \, \Omega = 48 \, \Omega \]

### Final Answer
The resistance connected with the galvanometer to convert it into a voltmeter to measure 5V is \( R_s = 48 \, \Omega \).

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