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. `4xx10^(-1)V`
B. `2xx10^(-3)V`
C. `4xx10^(-3)V`
D. `4xx10^(-1)V`

Answer

To find the error in the measurement of the e.m.f. when a voltmeter is connected to a cell with a given internal resistance, we can follow these steps:

### Step 1: Understand the Circuit
We have a cell with an e.m.f. (Electromotive Force) of 2 volts and an internal resistance of 2 ohms. The voltmeter has a resistance of 998 ohms.

### Step 2: Draw the Circuit Diagram
Draw a simple circuit diagram showing the cell, its internal resistance, and the voltmeter connected in parallel to the internal resistance.

### Step 3: Calculate the Total Resistance
The total resistance in the circuit when the voltmeter is connected can be calculated as:
\[ R_{total} = R_{internal} + R_{voltmeter} = 2 \, \Omega + 998 \, \Omega = 1000 \, \Omega \]

### Step 4: Calculate the Current in the Circuit
Using Ohm's law, we can find the current flowing through the circuit:
\[ I = \frac{V}{R_{total}} = \frac{2 \, V}{1000 \, \Omega} = \frac{2}{1000} = \frac{1}{500} \, A \]

### Step 5: Calculate the Measured Voltage
The voltage measured by the voltmeter (V_m) can be calculated using the formula:
\[ V_m = I \times R_{voltmeter} = \left(\frac{1}{500} \, A\right) \times 998 \, \Omega = \frac{998}{500} \, V \]

### Step 6: Calculate the Measured Value
Calculating the measured value:
\[ V_m = 1.996 \, V \]

### Step 7: Calculate the Error in Measurement
The error in measurement can be calculated as:
\[ \text{Error} = \text{Actual Value} - \text{Measured Value} = 2 \, V - 1.996 \, V = 0.004 \, V \]

### Step 8: Convert to Millivolts
To express the error in millivolts:
\[ \text{Error} = 0.004 \, V = 4 \, mV \]

### Conclusion
The error in the measurement of the e.m.f. is 4 mV.