A : The displacement current goes through the gap between the plates of a capacitor when the charge on the capacitor does not change.
R : Displacement current arises only when the electric field is constant.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided in the context of displacement current in capacitors.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "The displacement current goes through the gap between the plates of a capacitor when the charge on the capacitor does not change."
- Displacement current (Id) is defined as \( Id = \epsilon_0 \frac{d\Phi_E}{dt} \), where \( \Phi_E \) is the electric flux. It is also related to the rate of change of charge on the capacitor plates: \( Id = \epsilon_0 \frac{dq}{dt} \).
- If the charge on the capacitor does not change, then \( \frac{dq}{dt} = 0 \), leading to \( Id = 0 \). Therefore, the assertion is incorrect.

2. **Understanding the Reason (R)**:
- The reason states that "Displacement current arises only when the electric field is constant."
- This statement is also incorrect. Displacement current arises due to a changing electric field, which is related to the changing charge on the capacitor plates. If the electric field is constant, then there is no change in electric flux, and consequently, no displacement current.

3. **Conclusion**:
- Since both the assertion and the reason are incorrect, we conclude that the correct answer is that both the assertion (A) and the reason (R) are false.

### Final Answer:
Both the assertion (A) and the reason (R) are incorrect.