A : The voltage across a battery may be less, equal or more than the emf of the battery.
R : Voltage across a battery also depends on the magnitude and direction of current .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark.
C. If Assertion is ture statement but Reason is false , then mark
D. If both Assertion and Reason are false statements then mark.

Answer

To solve the assertion-reason question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "the voltage across a battery may be less, equal, or more than the emf of the battery."
- This means that depending on the conditions in the circuit, the voltage (V) measured across the battery terminals can vary in relation to the electromotive force (emf, E) of the battery.

2. **Understanding the Reason (R)**:
- The reason states that "voltage across a battery also depends on the magnitude and direction of current."
- This indicates that the current flowing through the battery affects the voltage drop across it, which is influenced by the internal resistance of the battery.

3. **Analyzing the Circuit**:
- Consider a simple circuit with a battery of emf (E) and internal resistance (r).
- When current (I) flows through the battery, the voltage across the terminals (V_AB) can be expressed as:
- If the current flows in the forward direction (into the positive terminal), the voltage can be calculated as:
\[ V_{AB} = E + I \cdot r \]
This shows that the voltage can be greater than the emf (E) when current flows in this direction.
- If the current flows in the reverse direction (into the negative terminal), the voltage becomes:
\[ V_{AB} = E - I \cdot r \]
In this case, the voltage can be less than the emf (E).
- If there is no current flowing (I = 0), the voltage across the battery is equal to the emf:
\[ V_{AB} = E \]

4. **Conclusion**:
- From the analysis above, we can conclude that the assertion is true because the voltage across the battery can indeed be less than, equal to, or greater than the emf depending on the current's direction and magnitude.
- The reason is also true as it explains why the voltage varies with current.

5. **Final Statement**:
- Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion.