A voltmeter having a resistance of 998 ohms is connected to a cell of e.m.f. 2 volt and internal resistance 2 ohm. The error in the measurment of e.m.f. will be

Options

A. `4 xx 10^(-1)` volt
B. `2 xx 10^(-3)` volt
C. `4 xx 10^(-3)` volt
D. `2 xx 10^(-1)` volt

Explanation

To solve the problem of finding the error in the measurement of e.m.f. when a voltmeter is connected to a cell, we can follow these steps:

### Step 1: Identify the given values
- E.M.F. (Electromotive Force) of the cell, \( E = 2 \, \text{V} \)
- Internal resistance of the cell, \( r = 2 \, \Omega \)
- Resistance of the voltmeter, \( R_v = 998 \, \Omega \)

### Step 2: Calculate the total resistance in the circuit
The total resistance \( R_{total} \) in the circuit when the voltmeter is connected is the sum of the internal resistance of the cell and the resistance of the voltmeter:
\[ R_{total} = R_v + r = 998 \, \Omega + 2 \, \Omega = 1000 \, \Omega \]

### Step 3: Calculate the current flowing through the circuit
Using Ohm's law, the current \( I \) flowing through the circuit can be calculated as:
\[ I = \frac{E}{R_{total}} = \frac{2 \, \text{V}}{1000 \, \Omega} = 0.002 \, \text{A} \quad \text{or} \quad 2 \, \text{mA} \]

### Step 4: Calculate the voltage drop across the internal resistance
The voltage drop \( V_r \) across the internal resistance of the cell can be calculated using:
\[ V_r = I \cdot r = 0.002 \, \text{A} \cdot 2 \, \Omega = 0.004 \, \text{V} \quad \text{or} \quad 4 \, \text{mV} \]

### Step 5: Calculate the measured voltage across the voltmeter
The voltage \( V_m \) that the voltmeter measures is given by:
\[ V_m = E - V_r = 2 \, \text{V} - 0.004 \, \text{V} = 1.996 \, \text{V} \]

### Step 6: Calculate the error in the measurement
The error in the measurement of e.m.f. can be calculated as:
\[ \text{Error} = E - V_m = 2 \, \text{V} - 1.996 \, \text{V} = 0.004 \, \text{V} \quad \text{or} \quad 4 \, \text{mV} \]

### Final Result
The error in the measurement of e.m.f. is \( 4 \times 10^{-3} \, \text{V} \).

---