The displacement current flows in the dielectric of a capacitor when the potential difference across its plates-

Options

A. is increasing with time
B. is decreasing with time
C. has assumed a constant value
D. becomes zero

Answer

To solve the question regarding the displacement current in the dielectric of a capacitor when the potential difference across its plates is changing, we can follow these steps:

### Step 1: Understand the Concept of Displacement Current
Displacement current is a term introduced by James Clerk Maxwell to account for the changing electric field in the dielectric of a capacitor when there is a time-varying electric field. It is given by the equation:
\[ I_d = \epsilon_0 \frac{dE}{dt} A \]
where \( I_d \) is the displacement current, \( \epsilon_0 \) is the permittivity of free space, \( E \) is the electric field, and \( A \) is the area of the plates.

### Step 2: Analyze the Charging of a Capacitor
When a capacitor is charged, the voltage across its plates increases. This change in voltage leads to a change in the electric field \( E \) in the dielectric between the plates. As the electric field changes, the displacement current \( I_d \) also changes.

### Step 3: Determine the Behavior of the Potential Difference
1. **Increasing Potential Difference**: When the capacitor is charging, the potential difference across its plates is increasing.
2. **Decreasing Potential Difference**: If the capacitor is discharging, the potential difference is decreasing.
3. **Constant Potential Difference**: This would imply that there is no change in the electric field, hence no displacement current.
4. **Zero Potential Difference**: This means the capacitor is fully discharged, and there would be no displacement current.

### Step 4: Conclusion Based on the Options
Given the options:
- (a) Increasing with time
- (b) Decreasing with time
- (c) Assumes a constant value
- (d) Becomes 0

When the potential difference across the plates of the capacitor is increasing (during charging), the displacement current is also present and increasing. However, if we consider the scenario where the capacitor is discharging, the potential difference decreases, and so does the displacement current.

### Final Answer
The displacement current flows in the dielectric of a capacitor when the potential difference across its plates is **decreasing with time**. Thus, the correct option is (b).

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