Two cells of same emf but different internal resistance are connected in parallel so as to send current in same direction.
STATEMENT-1 `:` The equivalent emf of the combination is equal to individual emf of each cell.
and
STATEMENT-2 `:` The equivalent emf is the arithmetic mean of the individual emfs.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is True
D. Statement-1 is False , Statement-2 is True

Answer

To solve the problem, we need to analyze the statements regarding the equivalent EMF of two cells connected in parallel with different internal resistances.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have two cells, each with the same EMF (let's call it E) but different internal resistances (let's denote them as R1 and R2).
- These cells are connected in parallel in such a way that they send current in the same direction.

2. **Applying Kirchhoff's Law**:
- When connected in parallel, the voltage across both cells must be the same. Let this common voltage be V.
- For cell 1: The current I1 flowing through it can be expressed as:
\[ I_1 = \frac{V - E}{R_1} \]
- For cell 2: The current I2 flowing through it can be expressed as:
\[ I_2 = \frac{V - E}{R_2} \]

3. **Total Current in the Circuit**:
- The total current I flowing from the combination of the two cells is the sum of the individual currents:
\[ I = I_1 + I_2 = \frac{V - E}{R_1} + \frac{V - E}{R_2} \]

4. **Rearranging the Equation**:
- We can factor out (V - E):
\[ I = (V - E) \left( \frac{1}{R_1} + \frac{1}{R_2} \right) \]

5. **Finding the Equivalent EMF**:
- We can express the equivalent EMF (E_eq) in terms of the currents and resistances:
\[ E_{eq} = \frac{E}{R_1} + \frac{E}{R_2} \div \left( \frac{1}{R_1} + \frac{1}{R_2} \right) \]
- This shows that the equivalent EMF is not simply equal to the individual EMF E.

6. **Evaluating the Statements**:
- **Statement 1**: "The equivalent EMF of the combination is equal to individual EMF of each cell."
- This statement is **True** because the voltage across the parallel combination remains equal to the EMF of the cells.
- **Statement 2**: "The equivalent EMF is the arithmetic mean of the individual EMFs."
- This statement is **False** because the equivalent EMF is not the arithmetic mean but rather a weighted average based on the internal resistances.

### Conclusion:
- **Final Answer**: Statement 1 is true, and Statement 2 is false.