X-ray from a Coolidge tube is incident on a thin aluminum foil. The intensity of the X-ray transmitted by the foil is found to be `I_0`. The heating current is increased so as to increase the temperature of the filament. The intensity of the X-ray transmitted by the foil will be

Options

A. zero
B. `ltI_0`
C. `I_0`
D. `gtI_0`

Answer

To solve the problem, we need to analyze the relationship between the heating current of the filament in a Coolidge tube and the intensity of the X-rays produced.

### Step-by-Step Solution:

1. **Understanding the Coolidge Tube**:
- A Coolidge tube is an X-ray tube where electrons are emitted from a heated filament and accelerated towards a target to produce X-rays. The intensity of the X-rays produced is related to the number of electrons striking the target.

**Hint**: Remember that the filament in the X-ray tube emits electrons when heated.

2. **Initial Condition**:
- The problem states that the intensity of the X-ray transmitted by the aluminum foil is `I_0`. This is the intensity before any changes are made to the heating current.

**Hint**: Identify what `I_0` represents in the context of the problem.

3. **Effect of Increasing Heating Current**:
- When the heating current is increased, the temperature of the filament rises. This increase in temperature leads to a greater emission of electrons from the filament per unit time.

**Hint**: Consider how the number of emitted electrons affects the X-ray production.

4. **Relation Between Current and Intensity**:
- The intensity of the X-rays is directly proportional to the number of electrons hitting the target. Since more electrons are emitted due to the increased heating current, the intensity of the X-rays will also increase.

**Hint**: Recall the relationship: Intensity (I) ∝ Current (I).

5. **Conclusion**:
- Since the intensity of the X-rays increases with the increase in heating current, the new intensity of the X-ray transmitted by the foil will be greater than `I_0`. Thus, we conclude that the intensity will be greater than `I_0`.

**Hint**: Think about the implications of increased intensity in terms of the options provided.

### Final Answer:
The intensity of the X-ray transmitted by the foil will be greater than `I_0`. Therefore, the correct option is **Option 4**.