The validity of Ohm's law lies when:

Options

A. V is directly proportional to `I^2`.
B. V is inversely proportional to I.
C. V is directly proportional to `I^3`.
D. V depends on I linearly.

Explanation

To determine the validity of Ohm's law, we need to analyze the relationship between voltage (V) and current (I) in a conductor. Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, provided that the temperature and material of the conductor remain constant.

### Step-by-Step Solution:

1. **Understanding Ohm's Law**:
- Ohm's law is mathematically expressed as \( V = IR \), where:
- \( V \) is the potential difference (voltage),
- \( I \) is the current,
- \( R \) is the resistance of the conductor.

2. **Identifying the Relationship**:
- From the equation \( V = IR \), we can see that if the resistance \( R \) is constant, then the voltage \( V \) is directly proportional to the current \( I \).
- This means that if we increase the current, the voltage increases linearly, and vice versa.

3. **Evaluating the Options**:
- We need to evaluate the given options:
- **Option 1**: \( V \) is directly proportional to \( I^2 \) (This is incorrect as it suggests a quadratic relationship).
- **Option 2**: \( V \) is inversely proportional to \( I \) (This is incorrect as it suggests that as current increases, voltage decreases).
- **Option 3**: \( V \) is directly proportional to \( I^3 \) (This is incorrect as it suggests a cubic relationship).
- **Option 4**: \( V \) depends on \( I \) linearly (This is correct as per Ohm's law).

4. **Conclusion**:
- The correct answer is **Option 4**: \( V \) depends on \( I \) linearly.