The poten tial difference between the terminals of a cells is found to be 3 volts when it is connected to a resistance equal to its internal resistance. The e.m.f. of the cell is:-

Options

A. 3V
B. 6V
C. 1.5v
D. 4.5V

Answer

To solve the problem, we need to find the electromotive force (e.m.f.) of the cell given that the potential difference across the terminals is 3 volts when connected to a resistance equal to its internal resistance.

### Step-by-Step Solution:

1. **Understand the Circuit Configuration**:
- Let the internal resistance of the cell be \( r \).
- The external resistance connected to the cell is also \( r \).
- The total resistance in the circuit is \( R + r = r + r = 2r \).

2. **Apply Ohm's Law**:
- The total current \( I \) flowing through the circuit can be expressed using Ohm's Law:
\[ I = \frac{E}{R_{total}} = \frac{E}{2r} \]
- Where \( E \) is the e.m.f. of the cell.

3. **Calculate the Potential Difference**:
- The potential difference \( V \) across the terminals of the cell is given as 3 volts.
- According to the formula for potential difference:
\[ V = I \times R \]
- Here, \( R \) is the external resistance, which is equal to \( r \):
\[ V = I \times r \]

4. **Substituting for Current**:
- Substitute \( I \) from step 2 into the equation for \( V \):
\[ V = \left(\frac{E}{2r}\right) \times r \]
- Simplifying this gives:
\[ V = \frac{E}{2} \]

5. **Setting Up the Equation**:
- We know from the problem statement that \( V = 3 \) volts:
\[ \frac{E}{2} = 3 \]

6. **Solving for E.m.f.**:
- Multiply both sides by 2 to isolate \( E \):
\[ E = 3 \times 2 = 6 \text{ volts} \]

### Final Answer:
The e.m.f. of the cell is **6 volts**.