In a hot wire ammeter the deflection angle `theta` of the pointer is related with the current I as

Options

A. a. `I alphatheta^2`
B. b. `I alpha sqrttheta`
C. c. `I alpha tan theta`
D. d. `I alpha theta`

Explanation

To solve the problem, we need to analyze the relationship between the deflection angle \( \theta \) of the pointer in a hot wire ammeter and the current \( I \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The deflection angle \( \theta \) of the pointer in a hot wire ammeter is related to the current \( I \) flowing through the wire. The ammeter measures the current by the amount of heat generated in the wire, which causes it to expand and deflect the pointer.

2. **Using the Formula**:
The relationship can be expressed as:
\[ I = \frac{C}{N A B} \cdot \theta \]
where \( C \) is a constant related to the characteristics of the wire, \( N \) is the number of turns, \( A \) is the area of cross-section, and \( B \) is another constant.

3. **Identifying Proportionality**:
From the equation, we can see that \( I \) is directly proportional to \( \theta \). This means that if the angle \( \theta \) increases, the current \( I \) also increases linearly.

4. **Conclusion**:
Therefore, we can conclude that:
\[ I \propto \theta \]

5. **Choosing the Correct Option**:
Among the given options:
- \( I \propto \theta^2 \)
- \( I \propto \sqrt{\theta} \)
- \( I \propto \tan(\theta) \)
- \( I \propto \theta \)

The correct option is \( I \propto \theta \).

### Final Answer:
The correct relationship is \( I \propto \theta \).

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