In the experiment of calibration of a voltmeter, a 1.1 V standard cell gets balanced at 440 cm length of wire. The balancing length corresponding to a potential difference between the ends of a resistance comes out to be 190 cm. A voltmeter shows 0.5 V for this potential difference. The error in the reading of voltmeter will be

Options

A. `0.025 V`
B. `25 V `
C. ` 2.5 V`
D. `0.25 V`

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Identify the given values
- EMF of the standard cell (E) = 1.1 V
- Balancing length for the standard cell (L) = 440 cm = 4.4 m (convert cm to m)
- Balancing length for the resistance (L_r) = 190 cm = 1.9 m (convert cm to m)
- Voltmeter reading (V_v) = 0.5 V

### Step 2: Calculate the potential gradient (K)
The potential gradient (K) can be calculated using the formula:
\[ K = \frac{E}{L} \]

Substituting the values:
\[ K = \frac{1.1 \, \text{V}}{4.4 \, \text{m}} = 0.25 \, \text{V/m} \]

### Step 3: Calculate the voltage across the resistance (V_r)
The voltage across the resistance can be calculated using the formula:
\[ V_r = K \times L_r \]

Substituting the values:
\[ V_r = 0.25 \, \text{V/m} \times 1.9 \, \text{m} = 0.475 \, \text{V} \]

### Step 4: Calculate the error in the voltmeter reading
The error in the reading of the voltmeter can be calculated as:
\[ \text{Error} = V_v - V_r \]

Substituting the values:
\[ \text{Error} = 0.5 \, \text{V} - 0.475 \, \text{V} = 0.025 \, \text{V} \]

### Final Answer
The error in the reading of the voltmeter is **0.025 V**.

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