The emf of a cell is 6 V and internal resistance is `0.5 kOmega` The reading of a Voltmeter having an internal resistance of `2.5 kOmega` is

Options

A. 6 V
B. 10 V
C. 5 V
D. 0.5 V

Answer

To solve the problem, we need to find the reading of the voltmeter when connected to a cell with a given emf and internal resistance. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Emf of the cell (E) = 6 V
- Internal resistance of the cell (r) = 0.5 kΩ = 500 Ω
- Internal resistance of the voltmeter (R_v) = 2.5 kΩ = 2500 Ω

### Step 2: Calculate the equivalent resistance
When the voltmeter is connected across the cell, the total resistance in the circuit (R_eq) is the sum of the internal resistance of the cell and the internal resistance of the voltmeter:
\[ R_{eq} = r + R_v \]
\[ R_{eq} = 500 \, \Omega + 2500 \, \Omega = 3000 \, \Omega \]

### Step 3: Calculate the current in the circuit
Using Ohm's law, the current (I) flowing through the circuit can be calculated as:
\[ I = \frac{E}{R_{eq}} \]
Substituting the values:
\[ I = \frac{6 \, V}{3000 \, \Omega} = 0.002 \, A = 2 \, mA \]

### Step 4: Calculate the voltage across the voltmeter
The voltage reading (V) on the voltmeter can be calculated using Ohm's law:
\[ V = I \times R_v \]
Substituting the values:
\[ V = 0.002 \, A \times 2500 \, \Omega = 5 \, V \]

### Final Answer
The reading of the voltmeter is **5 V**.

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