Assertion : Potential difference across the terminals of a battery is always less than the emf of the battery.
Reason : During discharging of a battery potential differnce across to terminals of a battery is
`V = E -ir`
`therefore V lt E`

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true and Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze the assertion and the reason provided:

### Step 1: Understanding the Assertion
The assertion states that the potential difference (V) across the terminals of a battery is always less than the electromotive force (emf, E) of the battery. This is a general statement about batteries during discharging.

### Step 2: Analyzing the Reason
The reason given is that during the discharging of a battery, the potential difference across the terminals is given by the equation:
\[ V = E - ir \]
where \( i \) is the current flowing through the battery and \( r \) is the internal resistance of the battery.

### Step 3: Deriving the Relationship
From the equation \( V = E - ir \):
- The term \( ir \) represents the voltage drop due to the internal resistance of the battery when current flows through it.
- Since \( ir \) is a positive quantity (as both \( i \) and \( r \) are positive), it follows that:
\[ V < E \]
This confirms that the potential difference across the terminals is indeed less than the emf when the battery is discharging.

### Step 4: Conclusion
Thus, the assertion is true because the potential difference across the terminals of a battery during discharging is always less than the emf of the battery, as derived from the reason provided.

### Final Statement
- **Assertion**: True
- **Reason**: True
- The assertion is correct, and the reason correctly explains why the assertion holds true.